The practice of perspective, or, An easy method of representing natural objects according to the rules of art : applied and exemplified in all the variety of cases ... : the whole illustrated with one hundred and fifty copper-plates

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Or, An Easy
METHOD
: : Of REPRESENTING ae

|. NATURAL OBJECT
| .. According to the Rutes of ART. |
| Applied and Exemplified in all the Variety of Cafes; as LANDskIPs,

GaRDENS, BuiLDINGs, of divers Kinds their. “ppendages,
Parts, Furniture, &c.

With RULES for the Proportions, Pofitions, Gc. FIGURES,
both in DRAUGHT and RELIEVO,

Alfo the Manner of condu@ting the SHa Dow s by divers Luminaries; and Practical Me-
thods of DESIGNING truly, without underftanding any Rules at all,

A WORK highly neceffary for

PAINTERS,

ENGRAVERS, STATUARIES,
ARCHITECTS, JEWELLERS,
EMBROIDERERS, TAPESTRY-WORKERs,

And others concerned in DESIGNING.

The Whole illuftrated with One Hundred and Fifty Copper-Phares,

Written in French by a Jesut'r of Paris ; fince tranflated into German, by
Cru. Remsotp and into Engh/b, by Ros. Pricxr. And now, a fecond
Time, into the fame Language, by. Cuamepsrs, F. R. S.

The Tuirp EpirTi1on.

‘To which is prefixed the Theory of Per/peétive, in which the Reafonsand Grounds of the feveral
Methods made ufe of in the Practice are fhewed and demonftrated, by ‘ames Hodg/an, Fel-
low of the Royal Soctety, and Mafter of the Royal Mathematical School in Chrift Ho/pital.

Tf you would proceed immediately to the Practice of PerfpeCtive, without engaging in the Intricacies
of the Theory, the Jusuir’s PersPECTiys, will anfwer your Purpofe.
Wolfius in Element. Mathef, Tom. Il. p. 1048.

EON DO N:
| . Printed for I'uo, .Bowxnes, Print and Map-Seller in St. Paul’s Church-Yard ;

and Joun Bowxegs, Print and Map-Seller atthe Black-Horfe in Cornbill,
MDCCA.LUT,

The Practice Of Perspective:

g4@\ H E Principle or Foundation from which Persprc

& Tive arifes, isthe Eye; an Organ which Nature has
au) endued with a greater Share of Vivacity and other
2 Perfections, than the reft of theSenfes ; and which

even holdsthe fame Advantage over them, that the
Soul does over the Body. The like Advantage does the Artof
Perspecrive hold over the other Mathematical Arts ; being
confefiedly the moft elegant and agreeable, and affording more
Matter of Entertainment, thanall the reft. ’Tis the very Soul
of all Painting; and thatalone which can make the PA IN T-
ERa Mafter. “Tis this muft condué him in the Difpofitions,
Heights and Proportions of his Figures, Buildings, Moveables,

and other Ornaments. Tis this muft thew him what Colours

are to be deep, or feint, or vivid, or dull; where each is to
be applied ; what to be finifh’'d up, and what only touched ;
where Light is to be beftowed, and where not: Ina Word, ’tis
this begins and ends the Painting. Without the Affiftance of
Perspective, the beft Mafter muft make as many Faults as
A Strokes;

iV PREFAC BE.

Strokes: And efpecially in Buildings, and fome other Enrich-
ments; which are Things I find fome of our moft reputable
Painters fo horribly defective in, that this has been one great
Motive to my undertaking the following Work; wherein their
Errors will be fhewn, without naming the Authors; and No-
vices inftructed how to avoid the like. The moft confummate
Mafter is tied to the ftri& Obfervation of every one of thefe
Rules, on Pain of pleafing none but the Ignorant: And an
indifferent Painter may be told this to his Comfort, that if he
make himfelf a thorough Mafter of thefe Rules, he fhall be
able to do Wonders. :

THE ENGRAVER in Copper canno more do without
Perspective, thanthe Painter; as havingevery Thing to
do with the Graver, that the other does with his Pencil. From
Perspective he muft learn where to lean heavily, and
where lightly ; what muft be funk deep, and what foftned.
Add, that his Occafion for this Art is more important, as his
Pieces multiply to a much greater Degree than thofe of the
Painter: So that if artfully performed, his Praife will be the
greater ; and if otherwife, his Failing the more notorious ;
each Piece being a Sort of Mouth to vilify its Author.

THESCULPTOR andSTATUARY mutt here learn
the Heights both for the high, low, and middle Sight ; the
Slopes and Inclinations of Buildings, and other Bodies ; the
Angle for the Point of Sight ; and the Proportions and Di-
menfions of all Objects, near and remote. |

BY the fame Artthe ARCHITECT muft learn how to
make his Defigns intelligible in a litte Compafs: He may like-
wife raife one Part, and leave the other in its Plan, to thewthe
whole Conduét and Effect of his Work. By the way, having
mentioned Archite@ture, we muft obferve of how much Con-
fequence it is, for fuch as practife Pz rspecTivs, to be know-
ing therein; the fineft Pieces of Perspective being thole

of

of great and magnificent Buildings, raifed according to the
Order of Columns, allthe Beauty whereof depends on their
Mealures and Proportions, which muft be obferved with the
Jaft Exactnefs, otherwife they fhock and offend the Eye. Archi-
tecture, therefore, muft be ftudied heartily: Nor can it any
way be excufed, to be ignorant of the fame; confidering
with how much eafe it may be learned in Vitruvius, V: ignola,
Scamozzi, and fome others.

TO know the Orders of Columns, and their Characters, is
not enough: He mutt likewife underftand all the ufual Dimen-
fions of Buildings, and the feveral Parts thereof; as Doors,
Windows, Chimneys, &c. how to difpofe them to receive the
Lights to Advantage, that nothing may appear maimyd, or dark-
ly ; totake care that every Thing be well fupported ; that no-
thing be ufelefs; and that there be a Symmetry and Proportion
running throughout the whole. Without fuch Regulation, a
Piece of Perspective, far from pleafing the Eye, will
wound and offend it.

GOLDSMITHS, EMBROIDERERS, TAPES-
TRY-MAKERS, ENA MELLERS,andevenJ OINERS
and others who have occafion to make Defigns, are under the
ftrideft Obligations to apply themfelves to Pexsprctivs,
if they would do any Thing to deferve Applaufe.

T HE greateft Part of fuch as I have known well affected to
this Art have affured me, that they were difcouraged by the
great Number of Lines which moft Authors make ufe of to form,
and find the Places of their Obje&ts, or Figures. Others have
been caft off by the great Number of Obfcurities in the Rules
and Operations ; and particularly from the Inftrudions not be-
ing immediately annexed to the Figures; fo that in turning over
to find them, they were apt to forget what they wanted. Now
thefe Complaints have warned me to be more clear and me-
thodical in my Inftructions, which are plac’d immediately before

A 2 | + each

he oe ee od. Ce,

each Figure, that the Reader may have both the Rule and the
Example in his Eye at once. Through the whole I have accom-
modated myfelf to the Capacity of Learners; not perplexing
them withtoo many Demonftrations; nor ufing any Words but
fuch as may be underftood, at leaft in the Definitions, With
thé fameview I have follow’d the common Cuftom of attribut-
ing Qualities to certain Things which really have them not.
Thus, in confidering Diftance, or Removal, Ihave been fore’d
to fay, contrary to my own Sentiment, that ‘tisthe Pupil which
receives the Rays from Objects, as if they terminated therein ;
whereas ‘tis paft Difpute, that Vifion is perform’d on the Retina
at the Bottom of the Eye; and that the Rays only pafs thro’
the Pupil in the way thither: Which, to fome People, will ap-
pear a new Language, and not to be conceived. However,
being affured that fuch a Piece of Knowledge imported but
little to the Practice of Perspective, I have attributed to the
Pupil what really belongs tothe Fund of the Eye, the proper
Place of Vifion, where the Species of Objects are formed ;
tho’ there are others who refer this to the Cryftalline. The
Reader who requires farther Satisfaction as to this Point, may
confult Aguillo Scheiner, and Des Cartes.

THO Ihave ftrained every Nerve to render the Science
eafy, Idon’t doubt but there are feveral will find fome Difh-
culty at the Beginning. But whoever can furmount the farft
Difficulties may go on affured, that there is nothing but he
will underftand, and praétife ; provided he takes care to ma-
fter one Rule well before he turn over the Leaf to another.
The Truthis, they may be faid, in fome meafure, tohang and
depend on each other: And a little Trouble of this Kind, at
firft, will be abundantly recompenfed by the future Eafe ac-
cruing from it.

IT will appear from the following Table, that this Work a-
lone fuffices to carry youthro’ all the Stagesand Degrees of Pe r-

‘ , 6: SPECTIVE,

POR ef AGE, Vil

spECTIVE, and to perform all Kinds of Draughts; by only
having recourfe to the feveral Rules, which the Figures indicate,
and bringing and collating them together, to furnith out the
Thing requir'd. This, nodoubt, muft be agreeable enough to
a Perfon who defires to make a Draught, to find immediately
what may. anfwer his Purpofe: ‘The Satisfaction, afluredly, mutt
far tranfcend that of copying a Piece already done by another.
Add, that in cafe he be oblig’d to copy any other, he will doit
with much more eafe, by means hereof; inafmuch as we fur-
nifh Inftructions for every Thing that can occur. I confefs I _
take infinite Pleafure in making new Defigns, and inventing
new Figures; which I fhould have madepublick, as my Predé-
ceflors have done, but that I was willing every Perfon fhould
participate in the Pleafure of compofing from his own Fancy ;
having furnifh’d him with all the Means requifice thereto. Such
as choofe to decline that Trouble, will meet with Defigns enough
ready to their Hand, in Marolois, Vredeman, Urieffe,and others,
who have affected to fhew the Politenefs of their Genius in
this Way.

SO many fine Performances, I doubt, have help’d to render
many of our Painters toolazy to learn to do what they find rea-
dy done. All they afpire at, is, to copy them as well as they
can ; which were excufable, did they know how to ufe them
to the Purpofe: But their way isto copy without knowing.
And hence it is, that we have ufually as many different Points
in a Painting, as there are Objects, Lines, and Returns. Some
of them will let you fee the Bottom of a Thing that fhould on-
ly fhew the Top ; and others, rather than be fhort, will thew
both. Others, again, having feveral Figures to fhew ina Paint-
ing, will makethem all of the fame Height: Tho’ fometimes
they vouchfafe to difpenfe with that Rule, and make thofe in
the Fore-part lefs than thofe behind, to give Room, as they tell

us

Ds

Miko. PR BR FAO:
us, for the hind Figures to be feen: Which isto overturn both
Art and Nature at once. ? |
TO fatisfy the Curious, who are always inquifitive after the
Reafons of Things, and require Order and Meafure every
where ; I have divided this Work intofive Parts: In the fir/?
are delivered a few Definitions, Demonftrations, and Reafons,
which need no great Stock of Mathematicks, to be underftood,
and which yet give a deal of Light into the Subje@ in Hand.
Thence I proceed to fhew the Nature of the Point of Sight,
Points of Diftance, Accidental Points, Front Point, and Side
Point, Vifual Rays, Diagonals, Parallels, Perpendiculars, and
Bafe Line ; the previous Knowledge of which Things is ex-
tremely neceflary, before you come to the Figures, and con-
tribute exceedingly to the eafy underftanding the Inftru@ions
that follow. In the fecond Part we give the Methods of fhort-
ning and diminifhing Plans divers Ways; with feveral Formsof
Pavements which ordinarily ferve for the Foundations of Per-
{pective Draughts. Having given fufficient Inftru€tions for put-
ting all Sorts of Planes in Perspective, we proceed, In the
third Part, tothe Elevations of divers Objects, beginning with
the eafieft, which are Cubes, and other Bodies of feveral Sides,
or Faces: Thefe are follow’d by Walls, Doors, Windows, Ceil-
ings, Vaults, and Stair-cafes of divers Forms, all without Or-
naments, or Mouldings, that the Rules might be the lefs per-
plex’d witha Number of Lines which fuch Enrichments would
have render’d neceflary. After fhewing all the Buildings in
their Simplicity and Nakednefs, I go on to furnith them with
Columns, Cornices, and other Ornaments, whichadda Maje-
{ty and Grace. The Houfes, all built to the Roof, I thew how
that isto be manag’d, with variety of Coverings: Then ad-
vance to the Infides, and give Rules for the Furniture, Move-
ables, °c. Thefe are followed by InftruGions relating to
Streets, Gardens, Trees, Walks; which are Things that infpire
4. a Ga-

PRL PA F. 1x
a Gaiety, and render the Draughts more entertaining, This
Part is.clofed with two or three Contrivances for facilitating the
Bufinefs of Perspective, and even for making the fineft
Defigns, without knowing any Thing of the Rules of Art.
In the fourth Part we give the Meafures and Proportions of
Figures, both in Draughts and Paintings, their Poftures, Situ-
ations, and Horizons, both for flat Paintings, and Relievo’s.
The fifthand laft Part confiders natural Shadows, both thofe of
the Sun, Torch, Candle, and Lamp.

WHEN the Perspective of a Building, Garden, Range
of Trees, Pallifade, or the like, intermix'd with Figures, is
intended, [would recommend it to you, to sketch out what
relates tothe Perspecrive with a Pencil in the firft Place ;
which done, you will proceed with more Affurance to fix the
Heights of Figures, and other Gircumftances.

ONE Thing fome People will find to cenfure in this Work,
viz. Thatthe Points of Diftance in all my Figures are toonear
the Pointof Sight. But if this bea Fault, ’tisa voluntary one:
For my Defign being to teach, it was neceflary every Thing
fhould be fhewn, and the Reader let to fee where fo many Lines
were to terminate; otherwife he would have been left to his
own Conjectures, °Tis fufficient that I dire& the Learner to
place them farther off; and even fhew the Laws and Occafions
thereof. Norcan it be fuppos'd I fhould have madeany Difh-
culty of making them more remote, had not other Gonfiderati-
ons prevail’d withme: One of which was, to render the Book
as {mall, portable and cheap, as poflible. Had I follow'd the Ad-
vice of fome of my Friends, I fhould only have given a fingle In-
ftruction in each Leaf; which would havefwell’d the Book to a-
bout thrice its Bulk, without rendering it a whit the more
intelligible. |

SOME People affect to conceal the Names of the Authors
they have follow’d; and, as has been well obferv’d of a certain

one,

o) POR YY. FACE.

one, pilfer from private Perfons what they give to the Publick.
For my own fhare, I confefs, that having propos’d to write a
little Treatife of Perspective, I was willing to fee as many
as Icould on the fame Subje@ ; nor made any Scruple of bor-
rowing from any of them what 1 found to my Purpofe, with
an Intention of making an open Reftitution of all my private
Thefts tothe Publick. The firft Writer of aay account, is George
Reich, in Cap. X. of his Works. The next, ¥7&or, a Canon of
Toul, who gives usa Number of good F igures, but is too {paring
in his Inftructions. After him comes Whert Durer, who has
left us fome Rules and Principles, in Lid. IV. of his Geometry.
Then 7. Coufin, who hasan exprefs Treatife on the Art, where-
in are many valuable Things. After thefe come Dan Barbaro,
Vignola, Serlio, Du Cerceau, Sirigaty, Solomon de Caus, Maro-
lois, Vredement, Urieffe, Guidus Ubaldus, Pietro, Acolty, the
Sieur de Vaulizard, the Sieur De/argues, and lately Father WVi-
ceron, a Minim: All whom I have read, one after another,
and not without admiring their great and happy Induftry in
the Service of the Publick; efteeming it fufficient Honour for
me to imitate what they have done, and to be the unknown
Copift of their Works. Befide thofe already recited, there are
many others, whom I have never feen; which Multitude of
Authors muft be allowed an Argument of the great Efteem the
Art has always been in, as well as the fuperior Regard paid to
it by the prefent Age. Onthis Confideration, I cannot doubt
but the following Work will be favourably received; efpecial-
ly, asit brings along with it feveral new Rules, and Inftrudi-
onsfor putting in Perspective any of the Objects ordinari-
ly under our Senfes, and, by Confequence, of performing
whatever relates to that Art.

|

De as Oa

DIRECTING TO

The feveral Parts and Members whereof
any Perfpective Dr auGHurT is to confift.

oa pantsss ee RPRI2IEDIIP
s

Roaye ERSPECTIVE muft begin with Plans, and,
bn Gas Za NEN °
Bye; Of Courfe, with fuch as are the moft fimple and
t=O! eafy; among which is the Square, or Cube: The
ig-ese28 Method of making the Plan whereof is found in acai
meen" Pag. tg. and that of its Elevation in Pag. 44, 49. in Front, and
If an angular View be required its Plan is given in Pag. 20, “%s/-»#/.
and its Elevation in Pag. so,
To raifé the Walls of a Houfe, of the Palifades of a Gar- Walls andPat.
den, ac. fee Pag. §1, 52. where you have both their Plans, 4:
and the-Elevations,
_ Such as require the Infide of a Hall, of Chamber, in ax/fdeof a
front View, muft take the fame Pag. 51, 52. for the Walls ;*””
the following Page for the Doors; Pag. 54. for the Wins=Dars.
dows; and Pag. 77. for the Chimney. The Cieling they
will find in Pag. 31, 32, 33, and 34. If a Door isto be open,”
you have your Inftructions in Pag. 33. and the Page fallow.
ing gives a Window or Cafement open. The fame Rules are siveda oy
to be obferved when there are two or three Stories over each ??*"™" .
other, as in Pag. 76. ‘To afcend to thofe Stories, we furnith
Stair-cafesin Pag. 82, 83, and 84.
Floufes viewed on the Infide are ufually furnifhed with Stair-caZ.
Moveables ; moft Kinds whereof are fhewn in Pag. npveables,
a 96-———103.

ATABL E, &c.

96——103. The Proportions of Figures to be placed therein,
are found in Pag. 122, 123, 124, 125.
Infide of 2 To thew the Infide of a Church, a Plan muft be pitched on,
Coane: and put in Perfpective, according to the Inftructions in Pag.
eo ay, hats Re Walls tobe raifed, from Pag.s1. The Win-
ae a. dows made like the Arches of Pag. 62, or 54. Pillars and Pi-
Chun, afters to be taken from Pag. 48. Columns from 87. A Vault,
Vault. or Vaults, from Pag. 68——72. AndaDome, or Cupola, from
Dome. Pag. 74, 75. To enrich it with Cornices, Mouldings, and
Cornices and other Ornaments, have Recourfe to Pag. 88—_—_q€92. For Al-~
ssc tars, to Far, 21, 925 99, 24-
Outfdes of For Outfides of Buildings: The Doors, and Windows are
Buildings. petformed as in the Infides, fee Pag, 53, 54, and106. When
raifed to the proper Height, the Method of roofing and cover-
ing them will be found in Pag. 107, 108. And if a Cor-
nice, or other Ornaments be required, you have them in Pag.
Galleries. 8892. Arched Galleries, both within and without Side,
are fhewn in Pag. 63, 66, 67, and 106.
Street. If a whole Street of Buildings be required, you muft mul-
tiply the Houfes on either Side, as in Pag. 109. When Houfes
Honfes far of. are made pretty deep within the Draught, fee Pag. 110. In
large Squares, &c. frequent in Streets, in Perfpective, a Pyra-

‘Pyramid. tid may be erected, as in Pag. 80. Or fome other Statue, or
Figure, or a Pedeftal, as in Pag. gt, and 124.

Buildings When a Building is to be viewed by the Angle, you may

viewed by the rake its Plan from Pag. 19, 30, and 111. and manage the Ele-

Angle. Eo
in ie vation as taught in Pag. 50, and 111. which give Rules for

Doors and Windows therein.
Gardens. Gardens in Perfpeétive rejoice the Sight more than any Thing,
on Account of their Colour, the Variety of Objects, &c,
Their Plans are to be made, as in Pag. 35, 38, or 113. and
Arbours. Compartments contrived therein at Difcretion. If Arbours
be required, you are fupplied from Pag. 60, or 61. If you
Palifade. tather choofe Palifades, look to Pag. 51, and 52. And if
Alleys of Trees.you prefer a Grove, Thicket, or Walk planted with Trees,
to either of them, Pag. 112. furnifhes Variety of each. If
Fountains. Fountains, or Fets d' Eau be wanted Pag. 29. gives a Bafon,
and its Elevation as in Pag. 73. For Squares, or Beds, fee
Pag. 99, or 44. For Polygons, 45, or 46. For Statues, or
Figures, which make a fine Ornament for Gardens, take the
Meafures from Pag. 122, or 125. For Grotto’s, or Nitches,
a fee

ATABLE, &c. xiii

fee Pag. 74. For an Afcent out of one Garden into another,
you have divers Forms of Steps in Pag. 78, 79, 80, 81. In Steps.
fine, youare at Liberty to choofe whatever pleafes your F ancy,

and may range them all in the fame Piece, provided you avoid >
Confufion, and obferve the due Symmetry and Proportions,

If you would have®pen Shops, without any Thing in them Séps.
but the Walls, you are furnithed in Pag. 55. If you require
them fitted up with Drawers, Boxes, gc. look to Pag. 95, Boxes.
and 105.

Amphitheatres were antiently of more ufe in Paintings than 4mpbishea-
at prefént, for which Reafon I have chofe to omit them: And“
yet fhift might be made, by taking the Plan in Pag. 29, and
adding more Circles, according to the Number of Stories in-
tended. To raife the Stories, you are to ufe the Lines of Ele-
vation in Pag. 7 5.

For Fortifications, you have the Method. of diminifhing Fortifications.
their Plans in Pag. 39. and the Method of raifing them in
Pag. 114.

To give the Shadows to Bodies of all Kinds, both thofe oc- Sha.)
cafioned by the Sun, Candle and Torch, is thewn from Pag,

129. to the End of the Book.. .
Particulars fee in the following Fableof ContenrTs,

a2 THE

ON

D Efinitions, Names, and Terms of the
Points, Lines and Figures ufed in
the following Work Page 1
Sequel of the Definitions, Names and
Terms. 2
Methods of defcribing the Lines and Figures
above defined 3
Methods of defcribing the Figures 4
Of circular Polygons, which are Figures of
feveral Angles infcribed in Circles ib.
Of the vifual Rays : f
Why a Piece of Perfpeftive is feen better
with one Eye than with two ib.
Firft Definition 6
Second, third, and fourth Definitions 7
Why Objetis appear the nearer each other,
as they are more remote from the Eye 8
Why Oljeéts appear the /maller as they are
at the greater Diftance 9
Of the Horizon 11
Of the terreftrial Line 12
Of the Point of Sight, Point of the Eye,
principal Point, or Point of Per/peétive ib.
Of the Points of Diftance ib.
Of the accidental Points ib.
Of the Point of the Front 13
Of the Side Point ib.
Of the vifual Rays 14.

Bp NOT Ss

Of the Diagonals or Diametrals of their
Sections Page 14.

Of the Diftance, or Removal

Advert. 1. Relating to the Side-Point

Advert. WW. Of the Depths and Hollowings

i
Advert. Wl, Of the Meafures upon ihe

Bafe : : 17
Advert. 1V. Of the Bafe Line, and a fin-
gle Point of Diftance ib.
Advert. V. Not to deceive one’s felf in the
Meafures ib.
Advert. V1. Of afingle Point of Diftance
18
Advert, Vil, How to do without making
ufe of the Diagonal ib.
Advert, VIII. Of several Ways of foort-
ning or dimini/bing ib.
Of Plans viewed direfily, or in Front
Plans viewed obliquely, or fide-wife
Of a Triangle
Of the Pentagon, or Five-Angle
Of the Hexagon, or Six--Angle
Of the Heptagon, or Sept-Angle

19

. Of the Offogon, or Eight-Angle

Another Method for the Octogon
Of the Hemagon, or Six- Angle
Of the double O¢togon

ee :

CON TEN TS.

Of the double Hemagon
Of the Circle

Of the double Circle 29
A Plan of Squares viewed Angle-wife

Page 27
28

30

A Pavement of Squares viewed by the An-
le 31
oF Squares encompaffed with a Lift, or
Fillet ib.
Pavements viewed Angle-wife, encompa/sd
with a Band, or Fillet 32
Pavements of Squares view'd in Front, en-
compaffed with Lifts, or Bands, whofe
Squares are divided by the Angle ib.
Pavement of Squares viewed Augle-wife,
with Chains of Squares in Front 33
Pavement of Squaresin Front, with Chains
of Squares Angle-wife ib.
Pavement of OQétogons, intermixed with
Squares 34

Pavement of fingle Squares view din Front

ib.
Plan of a.Garden in Per/pettive 35
Plan of a Building in. Per/pective 36
Plan of a Church in Per[pettive a4
Plan of a Houfe.with a Garden 38
Plan of a Fortification in. Perfpetiive 39
An irregular Plan and Figure in Perfpec-
tive 40
Another Plan of a Church in Per/pective 41
Preliminary Infirudions neceffary to the
following Methods 42
Of the Line of Elevation,, ferving to give
the Heights of all Kinds of Objettsinall
Parts of the Plan 43
Elevation of a Cube in Perfpetiive 44
Elevation of a:Triangle 45
A Pentagon, or Five-Angle.in siniingt
i

The Hexagon, or Sin-Angle in Perfpettive
ib.
The Heptagon, or Seven-Angle in Perfpec-

tive 46
The Oftogon, or Hight-sdngle in. Rerfpec-
tive ib.

4 double Crofs in Per/petiive 47
4

A Stone fluted, or channelled far-wife, in
Perfpective Page 47
Of Pilafters in Perfpettive a
Of Pilafters viewed by the Angle ib.
Effett of the Difference of Horizons 49
Elevation of Objects viewed by the Angle
50

Toraife Objects of any Heights, and remove
them to any Difiance at Pleafure 51
Of Walls viewed in Front 52
Another Wall viewed by the Angle ib.
To place a Door in any part of a Wall at

pleafure ~ i
To draw Windows in Perfpettive 54:
Of Cielings 55

Another Difpofition of Cielings in Perfpec-
tive 57
Circular Gates. and Arches view’ d direéily

5

Round Arches over Pilafters view'd "
Front 60
Gothic Arch, or Arch in the third Point ib.
Sequel of the former Figure 61
Lo defcribe, and put in. Perfpettive, round
Arches and. Doors 62
To, defcribe and put in Perfpettive, double
Arches and,Gates, i. e. fuch as foew their
Lhickneffes 63
Another Method for circular Arches 64,
Arches viewed obliquely in Perfpective ib,
Flat Arches 65
Toraife Archesupon Pilafters or Columns 67
Gothic Arches ib.
To find crofs Vaults in Per/pective 68
To draw the fame Vault more accurately 69
To form narrow Vaults 70
AV ault on the Foot of the preceding Rules
I

yi!
Arches and Gates with three Sides 72

An Arch with five Sides Mp
Elevation of round Objeéts 73
Elevation of Pilafters ib

A Vault in Form of a Shell in Perfpeétive

74
Open, Domes, or Vaults in Perfpetiive 75
That

CONTENTS.

That a Number of Objects, and Plurality
of Stories, only admit of one Point’ of
Sight Page 76

To put Chimneys in Perfpective a9

Stairs in Perfpective 78

Stairs open, or perforated underneath 79

Stairs viewed in Front ib.

Stairs that fhew four Sides 80

Another Manner ib.

Stairs view'd fide-wife in Perfpective 8t

Stairs in a Wall in Per/pective ib.

A Stair-cafe with Landing-places in Per-
Jpective 82

Winding or fpiral Stairs in Perfpective 83

Squares with Circles therein, in Perfpec-
tive 84

Round Stairs in Perfpective 85

Round Steps view'd fide-wife ib.

Winding Stairs 86

Columns in Perfpective 87

Cornices. aud Mouldings in Perfpective 88

A large Cornice above the Horizon in Per-
Jpective 89

To find the Bottoms of large Projectures 90

Cornices and Mouldings below the Horizon

I

Cornices with feveral Returns 3 “3

Fhe Apertures of Doors in Perfpective

93
Aperiures of Cafements in Perfpectide

94
Apertures of Cafements with Embrafures
ib.
Divers other Apertures 95
Plans and firft Elevations of Moveables

96

Elevations of Moveables 97

To make the upper Part of Tables, Stools,
&c

i 98
Elevation of Buffets and Cup-boards 99

Elevations of Chairs 100
Another Method of putting Moveables in
Perfpective LOI
Maoveables placed without any Order 102
Moveables laid or tumbled on the Ground
103

Altars in Perfpective
Shops in Per/pective
Buildings viewed on the Out/fide
Roofs of Houfes in Perfpective
Sequel of the Roofs in Perfpective
To put a Street in Perfpective
That remote Objects do not fhew their
Thickne/s | I1O
Buildings view'd by the Angle III
Fo put Walks, with Rows of Trees, in
Per/pective 112
To put Gardens in Perfpective 113
Beds with Borders ib.
To put Fortifications in Perfpective 114
To make Defigns in Perfpective 11.
Reduction of Perfpective Draughts out of
Small into great, and out of great into
finall II
Apparatus to the univerfal Method of the
Sieur G.D. L. ry
An univerfal Method of performing Per-
JSpective, without having the Point of
Diftance out of the Painting, or Ground
of the Work, made publick by the Sieur
G. D. bi. SNe aa Bi
To give any precife Diftance requir’ d, with-
out removing the Point of Sight out of
the Piece 119
A very curious Method of drawing all Per-
Jpectives in the moft natural Manner,
without obferving the Rules 120:
Another elegant Manner of practifing Per-
Spective, without underftanding it 12%
Figures in Perfpective 122
for Figures that have the Eye in the Hori-
ZON ib..
For Figures that bave a low Horizon ib.
ForFigures that have a high Horizon 123
For Figures that have their Feet in the Ho-
1ZOM ib.
Figures raifed above the Plan 124
The Poftures of Figures in Perfpective 125.
Beafis and Birds in Perfpective ib

Page 104

Lo find the Height of remote Figures, where-

of the firft ison a Mountain near the
Eye 126
To

|

CONTENTS.

To give the natural, or any otber Height,
to Figures much elevated Page 127
To find in what Proportion Figures grow
lefs to the Eye, when placed over one an-

other ib.
Meajfures for elevated Figures 128
Origin of Shadows 129
Of the Difference of Shadows 130

To find the Form of the Shadows ab I

Shadows from the Sun

The Shadows of the Sun are equal in Ob-
jects of the fame Height, tho’ at a ni
tance from each other

Of Shadows, when the Sun is directly oh
poled to the Eye 134

For the Shadows of perforated ici

135

Shadows affume the Form of the Planes
they are caft upon 136
Io find the Shadows of Objects broader at
Top than at Bottom 137
Io find the Shadows of aie Iu me
from the Ground 138

To find the Sun’s Shadow for human Hl

Pag

An eal) Method of finding the Shade a
the Sun

Shadows from a Torch, Flambeau, duaile.
and Lam is

Of the Foot of the Luminary

To find the Shadows of a Torch on al he
Sides of a Room

The Shadow of an erect and inverted Py.
ramid by Torch-light Fig

The Shadow of a Crofs

To find the Shadows of round Objects i
Torch-light 145

Shadows on feveral parallel. Planes 146

Shadows of Cielings by Torch-light 147

To find the Shadow by the Foot of the Lu-
minar a

The Shadow doubled :

The Shadows of human Figures by T wb
light 149

The different Pofitions and Heighis of Sha-
dows by Torch-light 150

SOME

T H E

THEORY

2

O F

PERSPECT IF £.

By James Hodgfon, F. R. S.

DEFINITIONS.

i, ERSPECTIVE is the Art of defcribing on a plain Surface
the true Reprefentation or Appearance of any given Object, as feen
tig one determinate Point for any given Diftance and Height of
the Eye. !

2. Phe Deieaiies Table, or Plane, is that Surface whereon the Picture of the

Object is formed, according to the Rules of Perfpective as ABCF. See Fig. 1.

3. The geometrical or ground Plane is that Surface whereon the Perfpective

Table is fuppofed to ftand, asGIK L.

4. The Height of the Eye is equal to the Length of a Perpendicular let fall

from it to the ground Plane, asE H.

5. The Diftance of the Eye from the Picture is equal to the Length of a Per-
pendicular drawn from the Eye to the Perfpective Table, as E D.
6. The common Seétion of the Perfpective Table with the ground Plane is
called the Ground Line or Section, as A B.
7. The horizontal Line is a Line in the Perfpective Table or Pifture, parallel
to the Seétion or ground Line, and of the Height of the Eye above it, as MDN.
8. The principal Ray is the Line drawn from the Eye perpendicular to the
Table, and is therefore equal to the Diftance of the Eye from the Table, as ED.
A

ge

ie

2 T THEORY

9. The Diftance of any Point in the ground Plane from the Table is a Per-
pendicular drawn from that Point to the Ground Line or Section, as Q T.

10. Direét parallel Lines are fuch as cut the Ground Line or Section at right
Angles, as Q T and S O. :

11. Oblique parallel’ Lines are fuch as cut the Ground Line or Section at
oblique Angles, as X T and Y Z.

12. Tranfverfe parallel Lines are thofe Lines which cut the direct parallel
Lines at right Angles, as PR and QS.

13. Radial Lines, or Vifual Rays, are fuch as run up from Points on the ground
Line, and unite in fome certain Point in the horizontal Line, namely, either in the
Point of Sight or in an accidental Point, as DT, DZ, DO.

14. The Point of Sight is that Point in the Picture, which is found by draw-
ing a Perpendicular from the Eye to the Perfpective Table or Picture, in which all
the direct Rays concur as the Point D.

15. The accidental Point is that Point in the Picture, where Lines that fall
obliquely on the ground Line or Seétion, but parallel amongft themfelves, unite.
or concur as the direct Rays do in the vifual Point, asthe PointE. See Fig. 2.

16. The Point of Diftance E is a Point in the horizontal Line of the Table
or PiGture removed as far diftant from the vifual Point D in the 2d Figure, as the

pad at E inthe firft Figure is diftant from the Table or Piture ABC F, namely,

17. The Point of Incidence is a Point in the Ground Line or Section, where
a Perpendicular let fall from any Point in the geometrical Plane interfeéts it, as the
Point Tor Z. See Fig. 1.

18. The Perfpective of any Point is that Point in the Picture, where the
vifual Ray drawn from the Eye at E to any Point, as P, inthe geometrical or

ground Plane, interfeéts the Picture or Table as the Point p.

19. The Perfpective of a Line is the common Section of the Table or Picture,
and the imaginary Plane formed by an infinite Number of Rays flowing from the
Eye at E, and falling upon every Point of the Line RS to be reprefented, as the
Liner s.

20. The Perfpective of any Plane Figure is the Section of the Cone or Pyra-
mid of Rays, whofe Vertex is the Eye, and Bafis the Figure propofed, made by the
Plane of the Table or Picture.

21. The Perfpeétive of any Solid upon the Table or Picture is the aggregate
of the Perfpectives of all the Planes whereof the Solid is compofed.

22. The optick Angle, under which any Object appears, is formed by two
Lines drawn from the Center of the Eye, to the two Extremities of the Objedt,
and here it isto be noted, that the moft convenient Diftance of the Eye, from the
Extremities of the Obje@t fhould be nearly equal to the longeft Dimenfion of the
Object, whether Breadth or Height.

For as the Beauty of Perfpeétive depends upon the Point of Diftance, fo the
Eye ought never to be placed too near the Object, nor too far fromit, but ata

convenient Diftance; and never nearer to the Object than one half of the largeft

Dimenfion, for in this Situation the vifual Angle will bea right Angle or 90 Degrees ;

and as this is the largeft Angle that the Eye can well difcover at one caft, {9 if ‘a
3

PERSPECT EVE 3

be made lefs than 45 Degrees, the Object will be too much contracted, and the
Vifual Angle will be fo fmall that the Returns in Buildings would not be diftin-
guifhed, and the Whole would appear confufed, and therefore when the Vifual
Angle is about 60 Degrees, which agrees with the above-mentioned Limitation,then
the Obje&t is feen with the moft Advantage, and confequently in all Perfpedtive
Defigns they ought to come as near this Situation as poffible.

23. When the Projection of any Object is made on a Plane parallel to the
Horizon by Rays parallel and perpendicular to the fame Plane, the Reprefentation
of the Object in this Cafe is called the Ichnography of the Figure propofed, whence
the Bafe, Bottom or Platform, whereon a Body or Building 1s erected, is called the
Ichnography of that Building, fo that to project the Ichnographick Reprefentation
of any Building is to draw the exact Ground Plot of the fame Building ; thus the
Geometrick Ichnography of a Column is a Circle, of.a Pedeftal is a Square, &e.

24. When the Projeétion is made on-a Plane perpendicular to the Horizon
by Rays parallel and perpendicular to the Plane upon which the Object is repre-
fented, the Reprefentation in this Cafe is called the Orthography of the Figure
propofed ; thus the upright Front of any Building or Object is called the Ortho-
graphy of that Object or Building, fo that to draw the Orthographick Reprefen-
tation of any Object or Building is to draw the exact Front of the Object or
Building as it really is and appears to be.

25. But when the Reprefentation or Projection of any Object is made by Rays
flowing from the feveral Parts of the Object, as the Front, Top or Bottom, Side or
Sides, and uniting in one Point where the Eye is fuppofed to he placed, the Re-
prefentation of this Object (upon a Plane-placed before the Eye ftanding at Right
Angles to the Line drawn from the Eye perpendicular to the Object, and) formed.
by the Interfection of the feveral Rays with this Plane, is called the Schenography
of that Object, fo that to draw the Schenographick Projection or-Reprefentation
of any Object is to draw the Projeftion or Reprefentation of the feveral Parts of
that Object, as they will appear to the Eye fituated at a convenient Diftance from
the Object upon a Plane placed perpendicular to the Horizon, and in a proper
Situation to receive the Obje&t ; and how this is to be done, is the proper Bufinefs
of Per{pective. | |

AALILOM §.

1. The common Interfection of two Planes is a Right Line.

2. If two Right Lines meet in a Point, a Plane may pafs through them both.

3. If two or more Right Lines are parallel to each other, they will all be in
the fame Plane; that is, if a Plane pafs through any two of thefe, it will pafs
through all the reff,

4. If two or more parallel Right Lines are cut by another Right Line, there .
may be a Plane that will pafs through them all.

5. If two parallel Planes are interfected by another Plane, the common Inter-

‘fections will be parallel to each other.

2 ue 6. Lines

4 | Th THEORY

6. Lines parallel to the fame Right Line, or to parallel Lines, are parallel one
to another ; conceive the fame of parallel Planes.

7. Every Point inany Right Line is in any Plane that Line is in.

8. A Space feen under a lefs Angle appears lefs, and the fame Space feen un-
der a bigger Angle appears bigger, and confequently Spaces feen undér equal
Angles are equal amongft themfelves. ;

N. B. Jn this Axiom we fuppofe the Spaces viewed ftand at Right Angles to.
~ the Axis or principal Ray ifluing diretly from the Eye, or which is the fame
Thing, that they are parallel to the Perfpective Table, for in other Cafes, where
the Diameter of the Object is inclined to the Table, it will not hold good.

THEOREM OL

If the Eye be placed any where between two parallel Right Lines, the farthet-
thefe Lines are produced from the Sight, the nearer they will feem to approach
each other. See Fig. 3.

Let S reprefent the Seat of the Eye, E M and Q_N the two given parallel
Lines, and S V the Axis or principal Ray, through the Points AC and M draw
the Lines AB, C Dand MN perpendicular to the principal Ray S V, and thefe-
Lines will be parallel and equal to each other. Alfo from S, the Point of Sight, let-
the Rays S A, SB, SC, SD, SM, S N be drawn.

Demon. Becaufe the right angled Triangles S Q B, SQ D, have the Perpendi-
cular SQ common to them both, but have the Bafe QD of the Triangle SQ D,
greater than the Bafe Q B of the Triangle SQ B, therefore the Angle SD Q,.
of the Triangle S Q D, will be lefs than the Angle S B Q of the Triangle SQ B:;
confequently the Angle PS D, which is equal to SD Q, will be lefSthan the
Angle O S B, which is equal to S BQ, and confequently: the double of the Angle
PSD, or the Angle CS D, will be leffer than the double of the Angle OS B,
ot the Angle A S B, wherefore the Line C D will appear lefs than A B by the 8th
Axiom, and confequently the Points.C and D of the Parallels E Mand Q N will
appear to the Eye placed at S nearer than the Points A and B of the fame Parallels.
EM and Q N.After the fame manner it may be proved that the Line M N,which
is. placed farther off from the Eye at S than the Line CD, will appear lefs
than C D, and confequently the Points M and N will feem to approach nearer to
each other than the Points C and D which are nearer, and that the fame Line
M N being placed at agreater Diftance than S V from the Point of Sight will ap-
peat leffer, and: confequently the Points Mand N in the laft Situation: will feem to
approach nearer to each: other than in the prefent Situation, and thus.fucceffively,
til] at laft the Line M: N)will appear indefinitely fmall, andthe Points;M.and.N will
feem to come together. os

Let us now fuppofe the Eye, fee Figure the 4th, placed above-the Plane'paffing
through the given Parallels, and let E Mand. Q N be the Parallels themfelves.

From H, the middle Point. of the Line E Q,, erect the Perpendicular H Sequal —
to the Height of the Eye above the Plane, then will S be the Place of. the Eye ;.

3 from

of PERSPECTIVE 5

from the Point S draw the Rays SE, SQ, SA, SB, &c. now becaufe the
Angles S E A and S Q B are right Angles, the Hypothenufes or Rays S A and
S Bwill be longer than the Perpendiculars S Eand SQ, and inafmuch as both
Triangles have the Sides SE and S Q equal to each other, it follows that the
Angle Q S E will be greater than the Angle B S A, and confequently the Line A B
will appear lefs than the Line EQ by Axiom the 8th, and the Points A and B
will feem to be nearer to each other than the Points EK. and Q , and by the fame
way of Reafoning it will follow, that the Angle D SC will be lefs than the Angle
BS A, confequently the Line C D will appear lefs than the Line AB, and the
Points Cand D will feem to come nearer to each other than the Points A and B,
&fc. which was to be demonftrated ; and the fame Ccn‘equences will follow if we
fuppofe the Point S placed below the given Plane of Parallels. -

Let us now imagine. a Plane, as E M N Q, to pafs through the Parallels E M
and Q_N, it is manifeft that to the Eye placed in the Plane itfelf or above or
below it, as in Figure the 4th, the two Extremities M and N which are fartheft
from the Eye will appear the neareft to each other, and the farther they are pro-
duced the nearer they will approach, till at laft being indefinitely produced,
they will feem to meet in a Point, and the Diftance will vanith.

And the fame Confequence will follow in whatfoever Situation the Plane is placed,.
whether it be perpendicular to the Horizon,or parallel to it, or inclined to it at any
given. Angle.

Hence we fee why Rows of Trees, of Columns, of Pilafters, why Walls and
the Sides of Buildings contraé&t themfelves and feem to grow narrower and nar-
rower the farther they are extended from the Eye.

Hence we fee the Reafon why Floors, and Pavements of Buildings feem to rife.

upwards towards the. Eye of the Spectator, as is very vifible in long Rooms or

Galleries, and why the Cielings feem to fink gradually downwards towards the Eye,,
whilft the Sides of the fame Building fee to come clofer and clofer, that the

Right-fide feems to approach towards the Left, and at the fame Time the Left-.

fide feems to approach toward the Right-fide, each Dimenfion growing leffer and
lefler,, and approaching nearer and nearer, the longer the Room 1s, till at laft if
the Length be indefinite, they will all vanith into the Vifual Point.

Hence we fee the Reafon why the Horizon appears higher than really it is, and.
that the convex Surface of the Sea to an Eye placed upon it appears curved and.
protuberant, and different from what it really is in itfelf. And,

Hence we fee alfo the Reafon why Statues and Pi@ures placed at a confiderable
Height above the Eye, alfo why Ornaments placed upon the Tops of Churches
or other publick Buildings appear fo much fmaller than really they are, as well in
Breadth. as in Height, and hence are drawn Rules for giving them their due Pro-
portion of Magnitude according to the feveral Stations allotted them, alfo for Por-
traits drawn upon Cielings or fet up at any confiderable Height, and for a great.
Variety of Appearances too many here to enumerate.

Now inafmuch as the vifible Magnitude of the Lines A O,C P, MV, fee Fm,
gure the 3d, or ther Doubles, namely the Lines AB, CD, MN, areas the
‘Tangents.of the optick Angles, ASQ, CS.P,M'S V, to the feveral Radi S O,

>»

~

6 The THEO 8:

SP, SV, or to their feveral Diftances from the Eye, it follows that the vifible

Magnitude of any Object increafes or decreafes in its various Approaches to or Re-

_ moves from the Eye in a reciprocal Proportion to its feveral Diftances from it:
And hence, |

The vifible Magnitude of any Body being given, and its Diftance from the
Speétator, the true Magnitude of the fame Body may be found, and on the con-
trary, the true or real Magnitude of the Objet being given, its vifible Magnitude
at any given Diftance may be determined; and hence we are taught to find of
what Magnitude any Object ought to be made to appear of a given Bignefs at a
given Diftance.

Thefe Laws extend to Objects that are placed above or below the Eye, as well
as to Objects that are placed upon the fame horizontal Plane with the Eye, provi-
ded they be placed at the fame Diftance from the Eye 5 but if they are erected
perpendicularly over the Plane, their Altitudes muft be increafed in the Propor-
tion of the Difference of the Tangent of the Angle of Elevation, and the Tan-
gent of the fame Angle of Elevation increafed by the optick Angle of the Figure
when viewed upon the horizontal Surface, and confequently the higher any Ob-
ject is placed above the Eye, the greater will be the Difference between the Tan-
gents of the feveral Angles of Elevation, and the Tangents of the fame Angles of
Elevation increafed by the horizontal optic Angle of the Figure, and confequently
the greater muft the real Magnitude of the Object be made to appear of the fame
Bignefs as if it was placed upon the fame horizontal Plane with the Eye.

THOR 2 aM.

If any Line in the Object be parallel to the Ground-line, its Perfpective in the
Pidture will be parallel to the Ground-line alfo.

Let MNO P, fee Figure the 5th, be the Piture or Perfpeétive Table, S the
Place of the Eye, and A B parallel to the Ground-line O P, the Line to be drawn
in Perfpective.

From S, the Place of the Eye, to the Extremities A and B of the Line A B let
the Vifual Rays S A, SB be drawn to cut the Perfpective Table in the Points a
and b. If thefe Points a and b be joined together by the right Line ab, I fay
this Line ab in the Table, which is the Perfpective of the Line AB the given
Object, will be parallel to the Ground-line O P. :

Imagine a Plane as K AB L to pafs through the Line A B, and to ftand at Right
Angles to the Plain C D R Q, now becaufe the Lines a b and A B are the common
Interfeétions of the parallel Planes MN O P, and ABKL, by the Vifual Plane
S A B, they will be parallel by the 5th Axiom, but A B is parallel to the Ground-
line O P by Hypothefis, therefore its Perfpeftive a b in the Table will be parallel
to the Ground-line alfo, by the 6th Axiom which was to be proved; and inafmuch
asthe fame Confequence will follow in whatfoever Place of the Plane C DQR,
the Line AB is feated, provided it be parallel to the Ground, Line AB, or
at whatfoever Diftance from the Eye the Plane CD R Q_is fixed, it follows
that all Lines, that are parallel to the Ground-line of any Picture will, when drawn

in

of PERSPECTIVE -

in Pefpeétive, be parallel toeach other and to the Ground-line alfo. Again, becaufe
theTrianglesS ab and S AB are fimilar, SX will be to Sx as A B toa b but S Xis
to Sx asS Zto S E, therefore, by a Similitude of Ratios, ab will be toA Bas
SE isto S Z, that is, the Length of the Perfpective Line in any Picture is to the
Length of its Original Line, as the Diftance of the Eye from the Picture or Per-
fpective Table to the Diftance of the Eye from the Plane of the original Object.

© I OR de he

The Perfpective of any Line, that is perpendicular to the Ground-line in the
Original Plane, will, when drawn on the Perfpective Table, run up into the Point
of Sight.

rie S, fee Figure the 6th, be the Place of the Eye, M N OP the Perfpective
Table, MN the horizontal Line, E the Vifual Point, O P the Ground-line, and
PR the given right Line cutting the Ground-line OP at right Angles in the
Point of Incidence P, I fay, if from P, the Point of Incidence, to FE, the Vifual Point,
the Line E-P be drawn in the Picture, the Perfpective of every Point R in the
given Line P R will be found fomewhere in the Line EP, in the PiGure.

Produce the Lines SE and R P toGand Q, and draw the Line SQ.

Becaufe SG and Q R are parallel, and the Line E P interfeéts them both in the
Points E and P, they will all be in the fame Plane SQ RG by the 4th Axiom;
and becaufe the Point of Sight S, and the Point R will be always found in this
Plane, the Perfpective of the Point R will always be found in the common Inter-
fection of this Plane S QR G, and the Plane of the Perfpective Table M N O P,
that is in the Line E P, and confequently in the Point r, where the Ray S R drawn
from the Eye at S to the given Point R in the Line P R interfeéts the Line E P
drawn from the Point of Sight E, to the Point of Incidence P, and confequently
if the Point R: were placed in the Point P, the Point P will be the Perfpective at
the Point R; and the farther the Point R is removed from the Point P, the higher
will its Perfpective r be in the Table, and the nearer wil! it approach to the Vifual |
Point E, till at laft, being removed at an indefinite Diftance from the Point of Inci-
cidence P; it will be projected in the Vifual Point E, and confequently the Line
FE Pin the Pi@ure will be the Perfpective of the Right Line PR, drawn perpen-
dicular to the Ground-line O P in the original Plane, and indefinitely produced,
which was to be proved. :

After the fame manner it may be proved that any other Right Line, as O D,
indefinitely produced, that cuts the Ground-line at Right Angles, will be reprefent-
ed in the Perfpective Table by the Line E O, drawn from the Point of Sight E in»
the Table to O, the Point of Incidence or Point where the Line O D cuts the
Ground-line. ,

Whence it follows, that all ftraight Lines in the original Plane, that cut the
Ground-line at Right Angles, will when drawn upon the Perfpective Table meet or
interfect each other in the Point of Sight.

THEOREM

Te THEORY

THEOREM W.

‘The.Perfpedtive of any Line in the original Plane, that cutsthe Ground-line at
oblique or unequal Angles, will be found in that Right Line that is drawn from
the Point of Incidence P, to the Point A in the horizontal Line of the Table,
which is found by drawing a Line, as S A from the Eye at S, parallel to the origi-
nal Line P R, till it interfe& the horizontal Line of the Table MN. See Fig. 7.

Becaufe the Lines S A and P R are parallel by Hypothefis, and A P interfeéts them
in the Points A and P, they will all be found in the fame Plane S A P R by the 4th
Axiom, and confequently the Perfpeétive of the Point R will be found in the
Table in the Point’ r, where the Ray SR hall interfeé&t the Line A P, the com-
mon Interfe@tion of the PlaneS A PR, and the Perfpective Table M N OP,
and if the Line P R be indefinitely produced from the Point of Incidence P, that
is, if the Point R be removed at an indefinite Diftance from the Point P, its Pers
{pective will be in the Point of the Table at A, that is, the Line A P will be the
Perfpective Appearance upon the Table of the Line P R produced indefinitely.

After the fame manner it may be proved, that any other ftraight Line, as O D,
indefinitely produced will be projected on the Perfpective Table into the Right Line
AO, drawn from the Point of Incidence O to the Pomt-found A, whence it
follows, that all ftraight Lines that fall obliquely on the Ground-line, yet if they
be parallel amongft themfelves, they will all unite or interfeét each other in fome
Point in the horizontal Line, and that Point is called the accidental Point ; and
to find it,

From the Eye Point S draw a Line parallel to. the original Line upon the ho-
rizontal Table, and where this Line cuts the horizontal Line it will give the ac-
cidental Point.

Hence it follows, that if the Eye be placed any where in the Line AS, pro-
duced from A towards S as far as you pleafe, the fame converging Lines on the
Table will be the Perfpectives of the fame Parallels in the Ground-plane, and
hence innumerable Points of Sight may be affigned for viewing the. fame Picture,
and hence we have a Solution of that Perfpective Paradox, that the fame Repre-
fentation of any original Obje& will be projected on the Table in the fame Lines,

though the Eye fhould change its Place and Diftance.

This Propofition is of very great Ufe, and therefore ought to be throughly un-
derftood, it being the main and principal Foundation of all the Practice im Per-
{pective, and indeed the preceding or third Theorem is nothing but a particular
Cafe of this general Propofition. Though I have given it a Place by its felf for
Order’s Sake, fince when the Lines on the original Plane fall at right Angles upon
the Ground-line, the Point of Concourfe of thefe Rays will be found by drawing
a Line from the Eye perpendicular to the Pi@ure, and this will neceflarily give the
Point of Sight to which all the Lines,that fall: perpendicularly upom the Ground-line
on the original Plane, muft neceflarily tend, as. has been proved in the third

T heorem.
ros {

sk eh And

|
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of PERSPECTIVE. 9

And in as much as the Line drawn from the Eye to the Point of Diftance upon
the Perfpective Table, muft-neceffarily form an Angle of 45 Degrees, with the
Principle Ray or the horizontal Line, the containing Sides of the Right Angle being
equal, it follows that the Diagonals of all Squares, one of whofe Sides is parallel
to the Picture, and all other Lines that form an Angle of 45 Degrees with the
Ground-line, will have the Point of Diftance upon the Table for their Point of
Concourfe ; and where, if produced upon the Table, they will all center.

TPE ORE MN:

The Projection or Perfpective of any Line, that is perpendicular to the horizontal
or Ground-plane, will on the Picture or Perfpeétive Table be perpendicular to the
Ground-line.

Let NM OP, in Fig. 8. reprefent the Perfpective Table, CDK Q_ the ho-
rizontal or Ground-plane, S the Place of the Eye, and AB the Line to be pro-
jected, which in the prefent Cafe is fuppofed to be perpendicular to the horizontal
Plane CD K Q, imagine the Plane R T ZX to pafs through the Line AB, and
to be parallel-to the Picture M N OP; now becaufe S B A is another Plane inter-
fe&ting the two former Planes, their common Seétions, or the Lines A B,a b, will
be parallel to each other by the 5th Axiom, but A B is perpendicular to the hori-
zontal Line X Z, therefore a b, if produced to G, will be perpendicular to the
Ground-line O P, which is parallel to the Line X Z, the Ground-line of the
Plane R T Z X. w. w. v.

And fince the fame Confequence will follow if the Line A B be fet upon any
other Point of the horizontal Table, it follows that the Perfpective Reprefentation
of all Lines, that on the Ground-plane are erected perpendicularly, will when pro-
jected on the Perfpettive Table be perpendicular to the Ground-line and parallel to
each other. And in as muchas the Linea b is to the Line AB, ass bisto SB,
that is,as S Eis to SL, it follows that ab, the Perfpective of A B, is to its Original
AB, as SE, the Diftance of the Eye from the Perfpective Table, toS L, the
Diftance of the Eye from the Plane of the original Object.

Again, through the Point a in the Picture, the Perfpective of the Point A in
the Ground-plane, draw x z parallel to the Ground-line O P, to cut the Rays S X,
SZ, in the Points x and z, then will x z in the Pidture be the Perfpective of the
Line X Z on the Ground-plane, and becaufe, by the Similitude of the Triangles
saxandS A X, it will beas A Xis toax, fo isS A tosa, andfosSEtoS L,
and foisa Eto aS, and foisabto AB; whence it follows that x ais to X A, as
abisto. A B, that is, any perpendicular on the Ground-plane is to its Perfpective
in the Picture, as any Parallel on the Ground-plane is to its Perfpective in the fame
Pidure, fuppofing the perpendicular and Parallel at the fame Diftance from
the Picture ; whence it follows, that if the perpendicular and the parallel are both of
the fame Length, their Perfpectives in the Picture will be of the fame Length alfo,
And this is a Property of no fmall Ufe in the Practice of Perfpedtive;. if nf

| B Length

~. - The THEORY
Length of any original Parallel or Perpendicular being known, it will be eafy by
the Help of a Sector to give any part of a Senographick Projection its Due Dimen-:
fions in any Situation upon the Table. _ |
Again, if from any Point S, in the. Line SF confidered as the Place of the
Eye, Rays, as SpB, Sq A be drawn to the Extremities of the perpen-
dicular AB, becaufe AB is topq, as SBis to Sp, that is, as SB is to Sb,
that is, as AB is toab, it follows that pq, andabare equal: Wherefore the
Diftance of the Objeé&t and the Eye from the Table, continuing the fame the
Perfpectives of the aa Perpendiculars, are equal to each other, whether the Eye
be placed at a greater or lefs Height above the Horizon.

PROBL & Mt

To find the Seat in the Perfpective Table of any given Point in the Original or
Ground-plane, the Height of the Eye, its Diftance from the Picture, and the
Diftance of the original Point from the Table being given. )

Let NM OP, See Fig. 9. reprefent the Table, S the Place of the Eye, SF,
its Height above the Ground-plane CDK R, SE its Diftance- from the PiGure,
Q the original Point in the horizontal Plane C DKR, and AQ its Diftance
from the Perfpective Table.

From S draw the Line SE, parallel to the Horizon or perpendicular to the Ta-
ble to cut the Table in the Point E, the Vifual Point in the Table, and from Q,
draw the Line Q A perpendicular to the Picture M N O P, to cut the Ground-line
in the Point A, the Point of Incidence. Now if a Plane as TSF Q., be ima-

ined to pafs through the Lines, ST, FQ, it will cut the Pefpective Table in the
Tine E A their common Interfection ; and in this Line of the Table will the Per-
{pettive of the Point Q be found, and confequently in the Point q ‘the Interfecti-
on of the Diagonal SQ drawn from S, the Point of Sight, to Q., the given Point
on the Ground-plane. ‘Let us now imagine the Plane of the Porecane Table to
revolve about the Line FA, the common Interfection of the two Planes till it
coincide with the Plane S T QF, asin Fig. ro. then will the Point Q in the
horizontal Table coincide with the Point Q in the Ground-line, the Pomt‘S
or Seat of the Eye in the Plane SF Q T will coincide with the Pomt S in the hori-
zontal Line of the Perfpective Table, and at the fame Diftance from the Vifual
Point E,as it was from the Perfpetive Table: In Fig. 9. in the like Manner, the
Diftance of the Point Q, in the Ground-line O P will be as far diftant from its
Point of Incidence A, as it was in the horizontal ‘Plane from the fame Pomt A,
for by this Revolution of the Plane of the Perfpective Table, the Poits‘S and
Q revolve about the Centers E and A, and confequently always keep the fame
Diftance from them, but the Line E A, the common Interfection of the ‘two
Planes M NOP, and S T QF becoming now the Axis about which the Plane
of the Table revolves remains the fame and immoveable, and confequently the
Seat of the Point Q in the Perfpective Table, remains in the fame Place as at firft
before the Plane was fuppofed'to revolve, and is therefore the true Perfpettive
Place upon the Table, which being allowed, we fhall have this general Rule. _

2

For

of PERSPECTIVE. ir

For finding the Seat in the Perfpective Table of any Point in the horizontal
Table. See Fig. 10. Namely,

1. From Q the given Point in the horizontal Table draw the Line Q A perpen-
dicular to the Ground-line to cut it in the Point of Incidence A.

2. Set off the Diftance A Q_ of the Point Qin the horizontal Line from the
Ground-line OP, from its Point of Incidence A in the fame Ground-line to Q.

3. From E, the Point of Sight, to A, the Point of Incidence, draw the Ray E: A,
and from S, the Point of Diftance, to the Point Q in the Ground-line laft found
draw the Diagonal SQ, and where this interfeéts the Ray E A laft drawn as in
the Point q, tt will give the Perfpective in the Table of the given Point Q in the
Ground-plane.

Now as every Line is bounded by Points, and every Surface by Lines, and
every folid by Surfaces ; hence we are. taught how to draw the Reprefentation of
any given ‘Object upon the Perfpective Table. And indeed the Laws here laid
down and demonftrated: are foigeneral, that whofoever. underftands them readily
will fee the Reafon of every Step taken in drawing the Scenographick Reprefenta-
tion of any original Object upon any Vertical Perfpedctive Table.

7M OR BM VL

If the Perfpeétive Table be inclined to the Plane of the Horizon at any given

“Angle, ‘the Perfpective-of any original Line, that is parallel to the Ground-line,

will in the Perfpective Table be parallel to the Ground-line alfo.

LetM NOP, in. Fig. 11. reprefent the Perfpective Table inclined to the hori-
zontal Plane C ABQ, at an Angle equal to MO A;3'let S be the Place of the Eye,
and A Bthe'Ground-line, whofe Perfpedtive is to be drawn, from S the Eye, let the
Vifual Rays S.A, S'B, be drawn to the Extremities A and B of the given Line
A B,to cut the Perfpective Table.in.the Points a and b; now if thefe'Points a and b
are connected together ‘by a Right Line ab, I fay, this Right Line ab, which is
the Perfpective of the original Lme AB, will be parallel to the Ground-line O P.

Imagine a Plane.as R A B T to pafs throught he given Line A By, and to be pa-
rallel to the Plane of the TableM NO P. |

Now becaufe the Lines ab and AB are the common Interfections of the
parallel Planes M N O'P, and RA BT by the Vifual Plane S AB, they will
be parallel to each other by the 5th Axiom ; but the original Line A B is paralleb
to the Ground-line O P by Hypothefis; therefore a b its Perfpective in the Table

~- wil ‘be parallel to the fame Ground-line.O'P alfo, ‘by the 6th Axiom. w. w. D.

Flence it follows that all Lines whatfoever, that upon the Ground-plane are
parallelto the Ground-line, theirPerfpetives upon the Picture will be Parallel to
the'Ground-line and to each other alfo.

Ra Ss ee

Thee THEORY

THEOREM VIL

In-any inclined Plane, the Perfpective of any Line in the original Plane, that,

being produced, will cut the Ground-line at oblique Angles, will be found in that
Right Line that is drawn from the Point of Incidence P. See Fig. 12. to the Point
A inthe horizontal Line of the Table, which is found by drawing a Line as S A
from the Seat of the Eye at S parallel to the original Line PR, till it interfeét the
horizontal Line of the Table M N.
Becaufe the Lines S A and PR are parallel by Hypothefis, and A P a right
Line interfeGting them both, therefore a Plane as S PRA will pafs through
them all, and therefore the Perfpective of the Point R will be found in the
Table in the Point r, the Interfeétion of the Diagonal SR, with the Line
AP, the common Interfeétion of the Plane of the Table M N OP, and the
Plane ASPR, confequently wherefoever the Point R be taken in the right
Line PR, its Perfpective will be found fomewhere in the Line AP, and
confequently the Line A P in the Table will be the Perfpective of the Line P R in-
definitely produced, fo that in whatfoever Part of the horizontal Plane the Line
P R be taken, provided it always forms the fame Angle with the Ground-line,
its Perfpective upon the Table will be always found in that Right Line which con-
neéts its Point of Incidence P on the Ground-line with its accidental Point A in
the horizontal Line. ;

If the Line PR cuts the Ground-line at right Angles, its parallel S A will in-
terfect the Table in the Point of Sight E upon the Table; wherefore in inclined
Planes as well as vertical Planes, as all Lines, that are perpendicular to the Ground-
line in the horizontal Plane, when drawn on the Perfpective Table, do run up and
unite in the Point of Sight, fo all other Lines in the Ground-plane that cut the
Ground-line when produced at unequal Angles, will if they are parallel to each
other when projected on the Perfpective Table run up and unite in one common
Point ; whence it follows that the Height of the Eye and its Diftance from the
inclined Table being known or given, the Perfpective Reprefentation of any ori-
ginal Ground-plane is drawn on the inclined Table by the fame Method, and after
the fame manner as it is done upon Vertical Tables. Let it therefore be required in,

PROBLEM &.

To find the Length of the principal Ray intercepted between the Point of Sight
and the Ground-line, or which is the fame Thing, the Height of the Eye in the in-
clined Table and its Diftance from the Table, the perpendicular Height of the Eye
above the Horizon, and the Inclination of the Perfpective Table being given.

Let O P, fee Fig. 13. reprefent the Ground-line, F QC a Line drawn at right
Angles to it, S the Seat of the Eye, SF its perpendicular Height above the
Ground-plane, and Q E the inclined Plane.forming an Angle with the horizontal
Plane equal to the Angle E QC.

2 3 From

of PERSPECTIVE 13
From Q the Point of Incidence of the Line E Q in the Ground-line, draw A Q_

perpendicular to the Ground-plane, and thromgh S the Seat of the Eye drawS A E

parallel to the Line F C to interfec&tthe Line Q E in E, then will E be the Point of
Sight in the inclined Plane, QE the Height of the Eye, and SE the Space
between the Vifual Point E. and the Point of Diftance S, whence the Perfpective
of any Ground Plot may be drawn on that Plane.

THEOREM VIL

In any inclined Plane,as M NOP, See Fig. 14. if from E the Point of Sight
through the Point b,where the Bafe F B of the Eye’s perpendicular Height S F cuts
the Ground-line of the Table, a Line as E b be drawn and produced till it cut S F,
the Line drawn from the Eye at S$ perpendicular to the horizontal Plane C QO P
produced downwards in the Point D, I fay the Perfpective of every Line perpendi-
cular to the horizontal Plane, will be found in that right Line in the Table that is
drawn from the Point D through the Point of Incidence made by a perpendicular
drawn from the Bafe of the elevated Line on the horizontal Plane to the Ground-lin
of the inclined Table.

Let MNO P be the inclined Perfpective Table, O P its Ground-line, where
it interfects the Ground-plane CR TQ, S the Seat of the Eye, SF its perpen-
dicular Height, E the Point of Sight in the Table, AB a Line perpendicular
to the Ground-plane, whofe Point of Incidence b is coincident with the Foot
b of the principal Ray Eb drawn on the Table; now if the Lines SF and Eb
are produced till they interfe@ each other im the Point D, I fay, that if from this
Point D through any other Point of Incidence as x in the Ground-line, a right Line
as D x z be drawn the Perfpective of the Line Z X ereéted perpendicularly over
the horizontal Plane, which Point of Incidence in the Ground-line is x, fhall be
found in this Line z x in the Table.

Becaufe the Lines S F D and ABW, are parallel by Hypothefis, a Plane as
SA BWDF will pafs through them, and becaufe the Eye is feated in this
Plane in the Point S, the Perfpective of the Line AB will be found upon
the Table in the Line E D, the common Interfe@ion of the two Planes, which
Line produced muft neceffarily cut the perpendicular S F, produced downwards
in the Point D, fince they all lye in the fame Plane. S Y WD.

Now if from this Point D a Line as Dx be drawn through x, the Point of Inci-
dence of the Line Z X erected perpendicular over the horizontal Plane CR T Q, 1
fay the Perfpective of this Line Z X will be found in the Line Dzx. -

For becaufe the LinesS D and Z X are’parallel by Hypothefis,a Plane as SZ XD
will pafs through them both ; and becaufe the Eye is feated in this Plane at S, the
Per{pective of the Line Z X will be found onthe Table in the Line xz, the com-
mon Interfection of the two Planes, which being produced muft neceffarily cut
the Line S D inthe Point D, the InterfeG@ion of the fame Line S D with the Plane
of the inclined Table produced, whence the Perfpectives of the Lines AB and ZX
on the Table will be the Lines a w and z q, intercepted between the Rays S A, S Z,
SX, and SB flowing from the Eye to the Tep and Bottom of the given Perpen-
diculars A B, and ZX. |

And -

14 The THEORY

And after the fame matiner may the Perfpective of any other Line elevated per-
pendicularly over the horizontal Plane be drawn on the Table.

For if we imagine a Plane to pafs through the Line S D perpendicular to the ho-
rizorital Plane indefinitely extended, and at the fame Time conceive this Plane te
revolve about the Line SD as an Axis, it will during the Courfe of this Revolu-
tion pafs through every Line that ftands perpendicular to the horizontal Plane, and
the fucceffive Interfections of this Plane with the Plane of the Table will be the
fucceflive Perfpectives of the feveral Perpendiculars it fhall happen to pafs through,
and as all thefe Lines muft neceffarily center in the immoveable Point D, as being
common to every Situation of the revolving Plane, it muft neceffary follow, the
Eye remaining alfo immoveable, that the Perfpective of ‘every Line, that is per-
pendicular to the Ground-plane, will be found in that Line in the Table which is
produced by drawing a Line from ‘this Point D, through the Point’of Incidence
mn the Groand-line made bya Perpendicular drawn from the Bafe of the'given elevat-
ed Line to the Ground-line of the inclined Table ; which was to be-demonftrated.

Hence and from the Rules demonftrated in Theorem 6, and 7. the Prattice of
drawing the Perfpective of Objects of any kind upon inclined Tables is eafily
deduced. :

By viewing the Figure, it is evident that the'greater ‘the Inclination of the Plane,

the leffer will be thie Angle SD E, and the farther will the Point D be removed
from the ‘horizontal Plane CR T Q, till at laft when the Plane becomes Vertical
the Point of Interfetion D vanifhes, and the Lines E bD and SF D become pa-
rallel, whence, as has been proved in'the 4th Theorem, it follows that all Lines that
are perpendicular to the horizontal Plane will, when projected on theTable, be ‘per+ —
pendicular to the Ground-line alfo.

‘Again, the farther the Point of Sight S is removed'from the Table, ‘the greater
will ‘be the Diftance of the Point ‘of Interfe@ion D from the horizontal Plane
CRTQ, till at laft the Eye being fuppofed at.an infinite Diftance the Line
SF D will be removed at an infinite Diftance from the Piéture, alfo the Point
of Interfection D will vanith, ahd the Elevation of all Lines perpendicular to the
horizontal Plane will become Perpendiculars to the horizontal Plane in the Table,
which is the Foundation upon which ‘the Military or Birds Perfpective is founded.

Again, the leffer the Inclination of the Table M'N O P, the ‘nearer does the
Point of Interfection D ‘approach to the Point F in the horizontal Table, the Foot
of the Eyesperpendicular, till’at laft when the inclined Plane M NO P coincides
with the horizontal Table'C R TQ, the Angle of Incidence vanifhes, and the
Point of Concourfe D coincides with the Point F ; whence it follows,

That in all horizontal or optical Projeftions, the Perfpective of*every Line, that
is erected ‘perpendicularly over the horizontal Table, will be found in that Line of
the Table which is produced by drawihg a Line'from the’Foot of ‘the Eye perpen-
dicular through the Bafe of the elevated Line ; wherice it follows that the Perfpec-
tive of all Lines, that ftand perpendicular upon the horizontal Plane, will if pro-
duced ‘unite or center in one common-Point, namely the-Point'wherea Line tet fall
perpendicularly thall interfecét the horizontal Table, i

THEOREM

]

OFPERSPECTTIVE 55
THEOREM

_. If the Plane of any. original Figure be parallel to the Table, .its Perfpedtive will
befimilarto its Original, alike, and alike fituated. _ |
_ Let §, fee Fig. 15. be the Seat of the Bye, MN.Q.P.the Lable, HI K.L the
Plane of the original Figure A B.C.D, ,
_ I fay, if the Planes M N OPand HIKL are parallel, the Perfpective Ap-
“pearance abcd upon the Table thall be fimilar to its original A B C D.
For from S the Point of Sight draw the RaysSa A, Sb B. ScC, and SdD.
Becaufe the Planes M N O Pand HI K Lare parallel, S A B is a Vifual Plane
interfecting them, therefore the common Interfeétions ab and AB will be parallel,
therefore A BwillbetoabasSBistoSb: Andagain, becaufe SB Cis aVifual Plane
terfeéting the fame parallel Planes, therefore their common Interfections, namely
the Lines B C and b c will be parallel, therefore B C will be to bc, asthe fame
Ray S Bis to the Ray Sb, wherefore by Equality of Ratios a b will be tob c, as
AB is toB C; after the fame manner it may be proved that bcistocd, asBCis
to CD, and cdistoda, asC D isto D A, whence the Perfpective F igure abcd
is fimilar to its original A BC D which was to be proved; whence it follows, that

. the optical or horizontal Perfpective of all Plane Figures that are parallel to the

Table, will be fimilar to their Originals ; that is, thatthe Perfpedtive of fquare
Figures parallel to the horizontal or perfpective Table, will onthe Table be fquare,
alfo the Perfpectives of Circles, will be Circles, of Hexagons, will be Hexagons, &#c,

Whence and from the laft Corollary of the preceding Theorem, the Reafons of
all the Appearances in horizontal Perfpective are manifeft, and as all Shadows are
nothing elfe but horizontal Projections of the feveral Objects, the Candle or lumi-
nous Body fupplying the Place of the Eye; hence it follows that every horizontal
Projection of any Object elevated above the Plane is the Projection of the Shadow
of the fame Object, and confequently the Rules given for forming of one will
ferve for forming the other. And inafmuch as the immenfe Diftance of the Sun
is infinite with regard to any terreftrial Object, hence it is that the Rays that flow
from the Sun to form the folar Shadow are fuppofed to be parallel ; and hence it
is that every Orthographick Perfpective of any Object elevated above the Plane of
the Horizon, is the Projection of the Shadow of the fame Body, and confequently
in drawing of one, you draw the other alfo; and thefe feveral Shadows, when
drawn upon the Scenographick Table according to the Rules of Scenographick
Projection, will exhibit upon the fame Table the Shadows of all Objects drawn upon
the Picture. :

Again, inafmuch as the Practice of horizontal Perfpective proceeds after the
fame manner as does the Practice of Scenographick Projections, fo in Praplem the
firft, Page the oth. | |

If we fuppofe the Eye in Figure 2. in S, the Point of Diftance in that Cafe,
and E. A to be the Diftance of the Eye from the given Object, the Demonftration
for one will hold good for the other, and confequently in proving the Operation
in one, you prove the Operation in the, other alfo,

Though

16 The THEORY, &c.

Though my principal View in this Tra& has been to render the Demonftrations
plain and concife, and the Number of Theorems as few as poflible, yet at the fame
Time I have endeavoured to make them fo general, that I may venture to fay there
is fcarce any Operation made ufe of in the Practice of the feveral Kinds of Per/peéfive
but what may be accounted for by fome one or other of the preceding Laws ; this
together with the following Treatife, which I look upon as one of the beft practical
Books of its Size that has appeared in the Exgli/d Language, will I hope make the

_ Whole as compleat and ufeful a Piece asthe narrow Bounds will admit of.

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PERSPECTIVE

CRUE EVUV ES GYGLOV ELEN,

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Definitions, Names and Terms of ¢be Points, Lines and Figures ufed ir
the following Work. |

A Pornr is that which is conceived to have no Parts; fuch as A, Fig. 1.
There are three Kinds of Points ufed in Perfpective, called Points of Sight
or View, Points of Diftance, and Contingent or Accidental Points.

ALrweisa Length without Breadth; fuch is AB, Fig.2. There are five
principal Lines ufed in Perfpective, viz. 1. The Line .of the Baje, calledalfo the
Line of the Plane, or the terreftrial Liae, asC D, Fig. 3. 2. The perpendicular of
plumb Line, which, falling on another, makes the Angles on either Side equal :
Such Angles are faid to be Right ones, and the Line fo falling on the other
called a Perpendicular thereto. Thus, in Fig. 3. A BandEF, falling no CD,
and making Right Angles in B andG, is a Perpendicular thereto. 3. The pa-
rallel Lines, which, being continued on the fame Plane to Infinity, never meet 3
as theLines N andiO, Fig. 6. The borizontal Line is ho more thana Line dtawn
parallel to the terreftrial Line ; as we fhall fhew more amply im its Place. 4.‘The
Diagonal Line, which is that drawn acrofs a Figure, from one Angle to another 5
fuch is K L, Fig. ro. 5. The occult Line, which is either drawn in Dots, or dry,
and is fuppofed not to appear when the Work is finifhed; fuch is O N, Fig. 2.

A Ricu T ANGLE we have already faid to be that formed by a Perpendi-
cular. ’Tis here reprefented a-part, by E. F G, Fig. 4. to fhew what it isthe more
diftinétly. There are two ‘other ‘kinds of “Angles, which comprife all thofe that
are not Right ones: The firft, called obtu/fe, are fuch as are.greater thana Right
Angle; as HLM, Fig. 5. The other, acute, are lefs than a Right Angle; fuch
as H I K in the fame Figure.

A Tz RM is the Extreme of any Thing: Thus the Points A and B, Fig. 2.
are the Terms of the Line A B.

A F1GuR £ is comprehended under one or more Terms: Thus 7, 8, 9, 13,
€Se, are Figures.

ASquare has its four Sides equal, and its four Angles Right; fuch is
ABCD, Fig. 7.

A PARALLELOGRAM, or long Square, has its four Angles Right, but
not its Sides equal; fuchis CDEF, Fig. 8...

An EquiLaTERAL TRIANGLE confifts of three equal Sides ; as GHI, Fig. 9.

The SecTion or INTERSECTION Of two Lines is when they run acrofs, or
«ut each other ina Point, as in Fig. 11. where AB and CD cut or interjed in E.

A Curve Liwe isthat which goes indirectly, or about, from one Point to
another; fuchis LM, Fig. 12.

A Circe isa plain Figure, comprehended under one fingle Line, called the
Circumference, to which all the Lines drawn from the Center are equal; fuch is
BCD, in Fig. 13. And the Point A in the Middle thereof is called the Center.

The DiameETER of aCircle isa Right Line BC, paffing through the Cen-
ter A, and dividing the Circle into two Parts.

AnOvat, or Etty ests, is an oblong Figure, comprehended under one
crooked, regular, but not circular, Line; fuch is E, Fig. 14.

ASprrRal, or VoLuT es, is a Line found by a Revolution about one or
two Centers ; fuch is F, Fig. 15. 3

FRENCTICA TH

2 PERSPECTIVE

LEBER RTT, TT ToS SCS OTOH TOTOT SOOT CTO SOG

SEQUEL of the Definitions, Names avd Terms.

T ANGENT isa Line, which being produc’d only touches or razes
an Obje@, Figure, or Line, without cutting it: Thus the Lines

AB are Tangents to the Circle C, in the Points DD, We here add
two kinds of Lines, which have the fame Denominations as the former,
and yet have different Effects, on account of the Point of View: For
the Angle EAB isto be efteem’d a right Angle, and all the Lines
CCC, &c. to be efteem’d as Perpendiculars to the Plane, as DF is;
and the Lines A B, GI, and HK, as Perpendiculars to the terreftrial
Line. © All the Lines drawn to the Point of Sight, whether from above,
or below, or from either fide, are called Rays, or VisuaLt Rays.

APLAN, IcHNOGRAPHY, orGROUND-PLAT, is a firft Draught
or Defign of a Thing, reprefenting the Traces or Paths of its Foundati-
on on the Ground, fo as to exhibit the Correfpondence, Situation, Di-
ftance, and Magnitude of the Parts, refpectively, at one View. This is
what we have reprefented in L and M.

A PotyGown isa Figure containing feveral Angles; as L.

ADEGREE is a little Arch or Portion of a Circle, whereof it con-
tains 360. Each Degree the Aftronomers fubdivide into 60 Minutes, and
each Minute into 60 Seconds, ¢ve. But fuch Subdivifion has no place here.
*Tis enough we know that Degrees are thofe little Divifions in the Circle »
NOP Q,, whereby Anglesare eftimated. From them we derive an eafy
Method of making all forts of Polygons, wz. by dividing 360 by the
Number of Angles the Figures areto confift of. Thus, for Inftance, if I
would make a Square, I divide 360 by 4, the Quotient is go, which
gives the right Angle NMO: And fo for the reft. Such as are unac-
quainted with Arithmetic, will find geometrical Methods of doing the
fame in Plate IV.

PRACTICA

PERSP EGQQIEY SE

Methods of Deferibing the Lines and Figures above defined.

exh dae raife Perpendiculars : If it be in the Middle of a Line that a Perpendicu-
lar is required, open the Compaffes to more than half the Length of the
Line, and fetting one Foot in the Point A, Fig. 1. with the other ftrike little
Arches both above and below, as F and F: The like do for the Point E, and the
two Interfections of thofe Arches will give a Perpendicular to the Line A E.

2. If the Line be at the Top or Bottom of a Draught or Paper, fo that Arches can-
not be ftruck both above and underneath, divide the Line into two, to get the
Point G, Fig. 2. and, from the two Extremes of the Line, make Arches in-
terfecting each other in H_; then draw a Line from H toG.

3. To raife a Perpendicular at the End of a Line, as at the Point J, of the Line
IK, Fig. 3. there are divers Methods: The firft is that already delivered. But
where room is wanting, one Leg of the Compaffes is.to be fet in the Point-I,
and with the other a large Portion of a Circle L M isto be ftruck, and the Com-
paffes,” thus open, to be fet on the Point M, and with the other Leg the Circle to
be cut in the Point N,; half the Arch M N being fet off from M towards O,
gives the Right Angle OI K: Or, without feeking for half the Arch M N,
from the Point N, defcribe an Arch P Q3 then, laying a Ruler over the Points
M and N, draw a Line, cutting the Arch P Q in the Point P, and raife a Line
from [to P ; which is the Perpendicular required. |

4. Or thus: If you would raife a Perpendicular from the Point P, Fig. 4. take
a Point, at Pleafure, over the Line PS, as the Point Q, and from this Point
defcribe a Circle paffing thro’ the Point P, and cutting the Line PS in fome
Place, as S ; then from S draw a Line thro’ Q to the Circumference of the Cir-
cle T, and the Point T gives the Extreme of the Perpendicular T P. A juft
Square fhortens all thefe Operations.

5. Tolet fall a Perpendicular froma given Point: From the Point, as A, Fig. 5.
defcribe the Arch BC, cutting the given Line E F in the Points G H, from
which Points defcribe two little Arches above or below, cutting each other in
the Point I; then, from the Point A let fall a Line thro’ Ito the Line EF,
and it will be the Perpendicular of the given Point.

‘6. From a Point given at the End of a Line to let fall a Perpendicular: Suppofe the
given Point K, and the Line LM, Fig. 6. from K draw a traverfe Line at
Pleafure, cutting the Line L M in fome Point, as N 3; divide the Line K N into
two equal Parts, and, from the middle Point O, draw an Arch thro’? K ; and
from the Point M, where it interfects the Line L M, draw the Perpendicular K P.

7. A Parallel Line, if truly drawn, will be a Tangent to Semi-circles drawn
from Points affumed in the other Line: Thus F G, Fig. 7. is parallel to H I,
becaufe it only touches or razes the Semi-circles L and K. :

8. Io divide a Line into equal Parts: Suppofe the Line be A B, draw another
Parallel thereto, either above or below it, as CD and on this laft, which is ei-
ther to be greater or lefs than that to be divided, fet off as many Partsas AB
is to be divided into, ex. gr. into feven ; from the firft and laft of thefe Divifions
draw Lines thro’ the Extremes of AB, interfecting each other in fome Point,
as E's from which Point drawing Lines to all the Divifions of the Line C D, the
Line AB will be divided into feven equal Parts.

PRACTICAL.

4 PERSPECT ?TV £
METHODS of Defcribing thé Figures.

1. fA Line as AB, Fig. 1, being given to form a Squareon, fet one Foot of the Compaffes in the
Point A, and extending the other the Length A B, defcribe the Arch B C; then from the Point
B defcribe another Arch A D, interfeéting the former in E, and from E fet off half the Arch E A, or
E B outwardly, to D and C; to which Points drawing Lines from A, B, Gc. the Square is form’d.
Or thus. Upon the given Line A B erect a Perpendicular A C equal to A B; then, taking the Length
A Bin your Compaffes, fet one Foot in B, and with the other defcribe an Arch © The like being done
from the Point C, the InterfeCtion of the two Arches will be the Point D, which gives the Square ABCD.
2. To deferibe a Parallelogram, or long Square, onthe Term E, of the given Line E F, ereét a Perpen-
dicular either greater or lefs than the fame, as EG; then taking EG in your Compafies, fet one Foot
in F, and with the other defcribe an Arch; take alfo E F in your Compaffes, and fetting one Foot in G,
defcribe a fecond Arch, cutting the former in H: This will give you the Parallelogram requir’d.

Of Circular Polygons, which are Figures of feveral Angles infcribed in Circles.

3. To deferibe an equilateral Triangle: The Compaffes being open to the Radius of the Circle, fet one
Foot in “the Poitt A, defcribe the Arch DE, and draw aright Line D E, which will be the Side of
the Triangle DEF.

4. For a Square, draw two Diameters at right Angles, and join their Extremes; thus you will have
the Square A B CD.

5. For a Pentagon, ox Five Angle, draw two Diameters, and take D G, half the Semi-diameter D I,
and from the Point G, with the Interval GA, defcribe the Arch AH ; the Chord of which is the
Side of the Pentagon.

6. For the Hexagon, or Six- Angle, the Semi-diameter is the Side of the Hexagon.

7. Por the Heptagon, or Sept Angle, take half a Side of the equilateral Triangle.

8. For the Offogon, or Eight-Angle, take half a Quadrant of the Circle

9. For the Enneagon, or Nine-Angle, take two thirds of the Semi-diameter for the Side ; as E B.

10. For the Decagon, or Ten- Angle, divide the Semi-diameter into two in the PointG, and from G,
with the Interval G A, defcribe an Arch AB; the Part of the Diameter B C will be the Side of the
Decagon.

1 a For the Undecagon, or Elewen- Angle, draw two Diameters at right Angles, and from the Point A,
with the Interval of a Semi-diameter, defcribe an Arch BC; then from the Point of Interfection C,
draw a Line to E ; the Portion C Dwill be the Side of the Undecagon.

12. Dodecagon, or Twelve- Angle, divide the Arch of a Hexagon, A B, into two equal Parts; the
Chord of the Moiety will be the Side.

13. 42 Oval is formed divers ways ; in all which the Figure is either a compound of {everal Portions
of Circles, or it is one Line drawn from two Centres. .The moft ufual Methods are thefe: Having de-
fcribed a Circle, and drawn two Diameters therein, as ABCD, from the Points AB we draw two
other Circles equal with the‘ firft; then from the Point D we draw a Line through the Center of the
laft Circle to the Circumference E : Thisdone, fetting one Foot of the Compafles in D, and with the
other taking the Interval E, we defcribean Arch EF. The like being done on the other Side, the Oval
is formed.

14. For a rounder Oval, draw afingle Line, and from A, as a Center, defcribe a Circle, the Inter-
fe&tion whereof with the right Line in the Point B, will be the Center of another Circle. Now, to form
the Oval, take in your Compaffes the whole Diameter of one.of the Circles, as from Ato F, andin one
of the Interfections of the Circles, as D, fetting one Foot of the Compaffes, with the other draw the
Arch GH: Thelike do from the Point E.

15. Otherawife we have an eafier and more ufeful manner of defcribing Ovals than any of the preced-
ing ones; thefame Rule ferving for all Forms, long, narrow, broad, fhort, Gc. Thus: Set two Nails
or Pins ina right Line A B, to ferveasa Center, and about thefe tie a Thread of the Length and Width
of- tne Oval required, as ABC; hold the Thread tight witha Pen or Pencil, and turn it about till you
arrive where youbegan. If you require it a long one, fetthe Centers the farther apart ; and obferve the
contrary for a fhort one: For if the Nails ftand clofe together, the Figure will be a Circle.

16. For a Spiral, or Volute, take two Pointsin a Line AB; the Points to ferve, one after another, as
Centers. For inftance, having drawn the Semi-circle A B, fetone Foot of the Compafles inB, and open
the other to the Length B A, and defcribe a Semi-circle A C; then fetting one Foot in A, take the In-
terval A C, and draw the Semi-circle C D 3. and this continuing as long as you pleafe, ftill fhifting Centers.
Viguola gives us another Method..

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PERSPEC PRY &E

OF he Visoan RAYS.

F an Object be a fingle Point, it fends only one vifual Ray to the Center
of the Eye; and that Ray iscalled the dxis, or Central Ray, as being the
moft vivid of all Rays: Such is A B,

If the Object be a right Line, the vifual Rays form a Triangle, as CAD,
whofe Bafe isthe Line C D, and Sides the twoextreme Rays ADand AC;
AB is thecentral Ray. _ If the Line were feen end-wife, it would appear as
a Point.

If the Object be a Surface, whether plane or fpherical, the vifual Rays
will make a Pyramid, whofe Bafis is the Object CDEF, and its Vertex
the Eye A. The reft of the Pyramid confifts of vifual Rays; in which
Number the Central A B is the ftrongeft, the others being all weaker, as
they are farther therefrom, though they ftill retain a competent Strength,
till they makea right-angled Triangle. Such as go beyond this, become
fo feeble, that they appear very confufedly. So that to have diftin@ Vi-
fion, the extreme Rays under which the Object is comprehended, muft,
at moft, fubtend a right Angle in the Eye. If the Pyramid were viewed
fide-wife, it would appear no more than a Line.

Why a Piece of PerfpeCtive is feen better with one Eye than with two.

Some hold that all Objects appear better with one than both Eyes; al-
ledging, that the Sight is render’d more penetrating by the vifual Rays of
the fhut Eye being determined to the other; inafmuch as‘all Powers be-
come more vigorous when united, than whendifperfed. Accordingly, fay
they, one of the Eyes being clofed, the whole vifive Virtue before diffus’d
thro’ both, is now fuppos’d to be collected into one; a Re-inforcement, .
muft neceflarily render it ftronger, more piercing, &c. than both.

Be this as it will, ’tis certain, we fee a Piece of perfpective with one
Eye better than with both. The reafon is, that the central Ray, in the
Cafe, is dire€ted to the Point of Sight where all the Radials of the Piece
do meet; which is what fhews a Pidture in its laft PerfeGion. ’Tis for
this reafon that we don’t fay, the Pornts of the Eyes, but, the Point of the
Eye, as infinuating, that Perfpective is moft pleafing, when viewed bya
fingle Eye. | 2

PRACT Te At.

6 PERSGQPECTUVE

COGKEGHOGHOG KIGHOGHOGIOGRIGKOSKOGHOIGHEGHOG) BOCGHEGHEGEIRIGKEGHOS HOSKINS EGR IKE

Firft DEEREIENITION.

ERSPECTIVE is the Art of reprefenting Objects feen through

fome tranfparent Medium, which the vifual Rays penetrate in paf-
fing from the feveral Points of the Object to the Eye. Accordingly,
whatever is feen through any Thing, as through Air, Water, Clouds, Glafs,
and the like, may be {aid to be feen in Perfpective. And fince we fee no-
thing butthrough thofe Mediums, ’tis certain all we {ee 1s in Perfpective.

The End of Perfpedtive is to exhibit Objects upon a Plane, fituate be-
tween the Eye and them, ex. gr. on the Plane EF GH, to reprefent the
Objeéts ABCD, in the Points IK LM.

The better ro conceive this, fuppofe an Objet ABCD on the Ground,
and a Speétator’s Eye in O; if a tranfparent Body EFGH be placed be-
tween the two, the InterfeGtions of the vifual Rays, with the Perpendicu-
larsQRST, will give the Figure 1 KLM, fuch as the Obje& appears on
that Plane. Perfpective, therefore, confifts altogether in the Interfecti-
ons of Lines: Whence it is, that Marolois always calls any Thing put in
Perfpective, the Appearance of the Seétion; fince the Plane EFGH
cuts the vifual Pyramid AC BD and O, and gives IK LM for its
Section.

The Reafon of thefe Sections is, that one fingle Line determines no-
thing; but there are two required to cut one another, to givea Point. Now,
as ’tis evident, that between our Eye and an Object, there is always a right
Line, or Ray, that can never be wanting: But to get the other, which is
to cut it, ’tis neceflary we conceive, that from our Foot as a Center, there
are a Number of Lines, or Rays, continually flowing to the Angles of the
Objeéts we fee ; as from P to the Angles ABC D: All which Rays being
cut by fome tranfparent Plane, as EF GH, the Rays PB, PA, PC, PD,
which before were horizontal, are now erected and become perpendicular:
PB, for Inftance, becoming QM, PD becoming. RL, &c. For if they
continued horizontal, the vifual Rays would never interfe&t them, ull they
both met in the Object itfelf. "Tis for this Reafon we always fuppofe a
Plane, which, reflecting the Rays, gives them an Occafion of interfecting,
and fo of finding the Points to form the Appearances of Objects, |

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7 PERSPECTIVE
CU IRI 8 ARR EIGIEN IRa
Second DEFINITION.

CunoGrapuy isthe Figure of the Platform, or the Plan
any thing. is to be rais’d upon: Thus ABCD is the /chno-
graphy, ot Plan, of afquare Body.

Third DEFINITION.

OrtTHoG RApuHyis the Figure of the Front or Fore-fide
of an Obje@, as an Houfe, &c. Or it is the Figure of an Ob-
ject, as a Houfe, &c. direétly oppofite to the Eye: Thus
EFGH is the Orthography, or, Fore-part, of a Cube, or |
Houfe. As the Ichnography reprefents the Plan, the Ortho-
graphy reprefents the Side oppofite to the Eye.

Fourth DEFINITION.

ScenoGRAPHY is what exhibits the Object quite rais‘d,
and perfect, with all its Diminutions and Shadows, both in
Front, the Sides which may be feen, and the Top: Thus
IKLMN OPisa Scenography, or perfect Cube. This is the
whole, and comprehends all the others as Parts.

To renderthe Terms more familiar, we fhall, for the future,
call the Ichuography Pian, the Orthography Front, and the
Scenography ELEVATION.

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Why Objects appear the nearer each other, as they are more
| remote from the Eye.

fe 1S Figure may help to folvea Queftion of fome Difficulty : Suppofe
a Spedtator’s Eye in the Middle of a Line at ++, ’tis evident, that if
it would fee the two Extremes thereof, A and B, it muft take in a Semi-
circle V X, whofe Center is in the Eye itfelf, and whofe central Ray is
the Line + T. By taking in this Semi-circle, ic will perceive the Ob-
jects on either Side, and in fuch manner, as that thofe fartheft off from
the Side A appear to approach towards the Center T, and thofe on the
Side B feem to approach likewife.

Now ’tis afked, How Things fo wide afunder fhould come to approach
and join each other, and that whether fituate fide-wife or over one an-
other ? |

The Anfwer in few Words is this: All Obje&ts appear under the vi-
fual Angle they fubrend at the Eye. Now, be they Columns, Trees,
Animals, or any other Things, placed on the Side of A, the remoteft will
feem to border on the Center T, by reafon they are feen under an Angle,
or Ray, that is near thereto. The Ray +- K, for Inftance, being much
nearer the central Ray T, than is the Ray 4+- Cand -+-E, and of Con-
fequence muft appear to be there: Add, that if the Objects were pro-
longed to Infinity, they would ftill approach nearer the central Ray T,
till {uch Time as they feemed contiguous therewith, and only to form
one Point together.

Now, in Perfpective, the Sides A K and BS don’t continue parallel,
but degenerate into vifual Rays, interfecting each other in the Point of
Sight, and by that Means giving the Diminutions of Objects. ‘Thus, for
Inftance, in the fecond Figure, the Eye being at a Diftance capable of
feeing the Line AB, from the two Angles AB arife two Rays, which
proceed to the Point of Sight T, which Rays A T and BT receive the
Interfections the Point of Diftance makes with the Objects, which all the
while contract themfelves proportionably ; as will be thewn in its Place,
By fuch Means the whole Parallelogram A K BS, and all the Objects on
either Side become reduced into the narrow Compafs AV, BX: And if
“the Eye were more remote, that Space would be ftill {maller, fince the
farther an Objeét is off, the fmaller it appears, as we fhall make appear
in the following Page. .

2

PRACTICAL.

PERSPECTIVE

ES NS IST PRESS I SS ES I

W hy Objects appear the fmaller as they are at the greater Diftance.

\W E have already obferved, that Things appear according to the Angle
wherein they are feen, and that this Angle is takenat the Eye, where
the Lines terminating the Object, meet. The Eye A, for Inftance, viewing the
Obje& BC, will draw the Rays AB and AC, which give the Angle BAC; fo
that an Object viewed under a greater Angle will appear large, and another under
aleffer Angle little. Now ’tis certain, that among equal Objects, thofe at the
greateft Diftance will appear under the fmalleft Angle ; confequently in all Per-
fpectives the remoteft Objects muft be made the fmalleft: For Example, if the
Eye bein A, the Object BC, which 1s the neareft, will appear the biggeft, be-
caufe feen under the greateft Angle; and the fecond, third, fourth, and fifth
Objects will all appear fmaller and fmaller, tho” really all equal, inafmuch as
the Angles diminifh in Proportion as the Objects recede. If the Eye were re-
moved intoM, KL would appear the largeft; and BC, in this latter Cafe, no
bigger than NO.

The fecond Figure is a Sequel of what we have advanced: For, fuppofing the
Objeéts to appear fuch as is the Angle they are feen in, it follows, that if fe-
veral Lines be drawn between the Sides of the fame Triangle, they will all appear
équal: Thus, all the Lines comprifed between the Sides ON, OP, of the Tri-
angle NOP, will appear equal to each other 5 and, as Objects comprehended
under the fame Angle feem equal, fo all comprehended under a greater Angle,
feem greater, and all under a {maller, fmaller.

Thus much fuppofed: If there be a Number of Columns, or Pilafters, to be
ranged in Perfpective on each Side of a Hall or Church, they mult of Neceffity
be all made under the fame Angle, and all tend towards one common Point in
the Horizon O: For Inftance, the Eye being placed in A, viewing the firft Ob-
ject DE; if from the Points DE you draw the vifual Rays DO, EO, they
will make the Triangle DOE, which will include the Columns DE, FG, Hi,
KL, MN, foasthey willall appear equal. :

What we have faid of the Sides, is likewife to be underftood of the Cielings
and Pavements ; the Diminutions of the Angles of remote Objects, placed either
above or below, following the fame Rule as thofe placed laterally. We need not
therefore add any Thing farther ; unlefs, that Care be taken there be as many
Squares or Divifions between the remoteft Objeéts as between the neareft: Wor in
that Cafe, tho’ diftant Objects be the clofer as they are farther from us, they will
appear in fome Meafure to preferve their Diftance ; thus, in BCDE, the In-
terval between the feur neareft Columns, thereare fixteen Squares, and no fewer
than fixteen between the four remoteft KLMN.

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T follows from what we have faid, that if you join two
Triangles, as in the laft Figure but one, for the Sides, and
two others, of the laft, for the Tops and Bottoms of an Ob-
ject, all four will terminate in one fingle Point A, which is the
Point of Sight, wherein all the vifual Rays meet. And this
will give a Proof of what we have advanced, viz. That
Objects diminith as they remove, the lower rifing, the upper
falling, and the lateral clofing or approaching: An Example of
all which we give in Fig. L which exhibits, as it were, Depths
and Diftances falling back, and receding from us, though all
equally near the Eye.

The Trees being ranged by the fame Law, have the fame
Effe& as the Columns, &%c. For being all comprehended in
the fame Angle, and the two Rows having each its own Angle,
and the Angles all meeting in a Point A, they form a third,
which is the Earth, and a fourth, which, if you pleafe, is
the Air; and thus afford an elegant Object, highly entertain-
ing the Eye.

We come now to fhew how you are to proceed in putting
any plane Body, or other Figure, in Perfpective. )

PRAGELGA.L. 10

la

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FAURUA UOTE

aii

Ir PERSPECTIVE

Sedu hdc dards ce ddd dbs Oe Buh ode tnd de Seduce nd dad dad deh

Of the HORIZON.

HAT we call the Horizon, in Perfpective, is only a Line given us by

the Height of our Eye: Thus, if we be raifed on an Eminence, as 1s
the firft Man, our Horizon will be high; if we be only our own Height, as is
the fecond Man, the Horizon will be our own Pitch ; and if we be feated or laid
along, as is the third, the Horizon will be low : So that ’tis the Horizon fhews
how high the Eye is above the Ground.

This, in Effect, is the principal Article in a Piéture, and that which directs and
gives Law to all the reft; both as to the Slope and Inclination of Buildings,
and to the Meafures and Heights of the Figures. This has occafioned a little
Difpute among our beft Painters ; fome of them holding thatall Paintings fhould
have their Horizon in the Work itfelf, and that Perfpective allows, where the
Painting is raifed very high above the Eye, that it have its particular Horizon :
The reft do not allow of fuch a fecond Horizon, but always ufe the natural one,
where-ever the Painting be placed; as imagining that the whole Height and
Breadth before them is, as it were, one large Painting, from which that which
is raifed above ought to take its Meafures. The Refpect we bear to the Pa-
trons of each Opinion will not allow usto determine between them ; efpecially,
as feveral good Authors have tolerated both. But, if my own Sentiments were
asked, I fhould make no Scruple to profefs myfelf of the Opinion of thefe
latter ; by Reafon every Thing in the Painting will thereby appear the more
natural.

In this Line are always found the Points of Sight and Diftance, and fome-
times the contingent or accidental Point. Tis this Line, in fine,” that feparates
Heaven from Earth, and that terminates the View; and it is always parallel
to the Bottom of the Piece, or the Plan the Object is placed upon: Whence it
appears that nothing ought tobe placed above the Horizon, but what furpafles
the Height of the Eye; andif an Object be fo high as that it furpafies this Hori-
zon, the Plan of the fame Object muft be placed below it: Thus, a Tree*or
Mountain may have its Top above the Horizon, but its Bottom muft be a good
deal below it.

Whatever is below the Horizon fhews its Top; but in Objects ever fo little
above it, the Topis invifible: Thus, the two Blocks A B, placed on the Ground
_ of the firft Figure, fhew their Tops, by Reafon the Horizon is over them ; but
in thofe of the fecond Figure € D, the Top does not appear; and much lefs in
thofe of the third Figure: Yet, in Reality, they are all of the fame Height, fo
that ’tis the Horizon makes all the Difference.

PERSPECPRIWE

Of the Terreftrial Line.

f Ecatuae py tiwed: Line, Base Lrwe, or Line of the Pian,
is the Line an Object is placed or ftands upon, whereof each Object has its
particular one, and the whole Draught a general.one. This is always parallel 0
the Horizon, as is feen in A B of the firft Figure; FG of the fecond, and NO
of the third; and fometimes ferves to determine the Lengths and Breadths, par-
ticularly that at the Bottom of the Piece, whereto all the’ Meafures are to be ac-
commodated, as will be fhewn hereafter. en

e

Of the Point of Sight, Point of the Eye, principal Point, or Point
of Perfpective.

HE Poirntof SicutT, of th Evz, PerspecTive, or PRin-
cr1PAL Point, is a Point inthe Axis of the Eye, or in the central
Ray, where the fame is interfeéted by the Horizon. Thus the Point E, in the
_ firft Figure is the Point of Sight in the Horizon C D, wherein all the vifual Rays
meet. Itis called the Point of the Eye, or ocular Point, becaufe directly oppofed
to the Eye of the Perfon who is to view the Piece.

Of the Points of Diftance.

Ro of Distance, or PorntTs of Distance, is a Point, or

Points (for there are fometimes two of them) placed at equal Diftance from
the Point of Sight. They are thus denominated, by reafon the Spectator ought to
be fo far remov’d from the Figure, or Painting, and the terreftrial Line, as,thefe
Points are from the Point of the Eye, and are always to be in the horizontal Line.
Thus HI being the Horizon, and K the Point of Sight, Land M are Points of
Diftance, ferving to give all the Shortnings. Thus, ew. gr. if fromthe Extremes
of the Line F G you draw two Lines to the Point K, and from the fame Points
draw two Lines to the Points of Diftance M and L, where thefe two Lines G L and
FM cut the Lines F K and G K, inthe Points X and Y, will be the Line of
Depth, and the Shortning of the Square, whereof F G is the Side and Bafe. The
Lines drawn to the Point of Sight are all vifual Rays, and thofe drawn to the
Points of Diftance, all Diagonals.

Of the Accidental Points.

OnTINGENT, or AccriDENTAL PoinTs, arecertain Points wherein

fuch Objeéts as may be thrown negligently, and without Order, under the
Plan, dotend to terminate. For this Reafon.they are not drawn to the Point of
Sight, nor the Points of Diftance, but meet accidentally, and at random, in the
Horizon. Thus, for Inftance, the two Pieces of Wood X and Y terminate in
the Points V V V V in the Horizon PQ, not in the Point of View, whichis R,
nor inthe Points of Diftance.S and T. Indeed fometimes the Objeétsrare fo ill
difpofed, that thefe Points muft be made out of the Horizon, as we fhall have
Occafion to thew hereafter. They ferve particularly in the Apertures of Doors,
Windows, Stair-cafes, and the like.

td

12

PRACTICAL

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13 PERSPECTIVE

ENRICO WEIDER ABH GN HERINE RIED BIE DIEDT
Of the Point of the F RON T.

HE Point of Direct Vizw, or of the Front, is

when we have the Objet direétly before us, and not.
more on one Side than the other ; in which Cafe it only fhews
the Fore-fide, and, if it be below the Horizon, a little of the
Top too, but nothing of the Sides, unlefs the Object be poly-
gonous. Thus the Plan ABC Disall in Front, and, if it were
raisd, we fhould not fee any Thing of the Sides AB, or CD,
but only the Front AD: The reafon is, that the Point of
View E, being dire@ly oppofite thereto, caufes a Diminution
on each Side; which, however, is only to be underftood where
an Elevation is the Object; for, if it be a Plan, it fhews the
whole, as ABCD.

BASS AG ASUS WG WS UG VO WG GAG WG AG UG UG 1G WAG AG 6 2G 2 AG ae
Of the SIDE Porn tT.”

TL HE Point of Osrique View, or of the Sipz, is
when we fee the Object afide of us, and only, as it
were a-flant, or with a Corner of the Eye; the Eye, how-
ever, being all the while oppofite to the Point of Sight: In
which Cafe we view the Object laterally, and it prefents us two
Faces, or Sides. For Inftance, if the Point of Sight be inF,
the Object G HIK will appear a-thwart, and fhew two Faces,
GK and GH; in which Cafe it will be a Side Point. ‘The
Practice is the fame in the Side Points as in the Front Points; ~
a Point of Sight, Points of Diftance, &c. being laid down
in the one as well as the other.
t )

PRACTICAL, _

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14. PERSPECTIVE
Of the Visi at Rays,

7 1 San univerfal Rule, That all the Lines which, in a geometrical Plan, are

erpendicular to the terreftrial Line, bealways drawn to the Point of Sight,
when the faid Planis to be put in Perfpective: Thus, in the little Plan AO, OB,
Fig. r. AB isthe terreftrial Line, to which allthe Lines Z, Z, &¥c. are perpen-
dicular. But if the Plan be tobe thrown into Perfpective, and either a greater
ora lefs Line than that of the Plan be pitched on, ew. gr. the Line AB, which
has the fame Number of Divifions as the fmallone, from the feveral Divifions Z,
the Lines are to be drawn direétly to the Point of Sight E. Such. Lines are pro-
perly denominated Radials and vifual Rays; and the Jatt of them, the Extremes,
as being drawn from the Extremities of the terreftrial Line AB.

Of the DIAGONALS, or DIAMETRALSOf ther Sections.

°T1s likewife a Rule, That all the Diagonals of Squares in the Plan be drawn,
in Perfpeétive, to the Point of Diftance: Thus, in the little Plan of Fig, 2. the
DiagonalsG O and F O are drawn to the Points of Diftance ; when the fame
Plan comes to be put in Perfpeétive, and by fuch Means the Shortnings or Dimi-
nutions of the Objeéts are got: So, if from the Extremes of the Bafe Line FG,
Lines be drawn to the Points of Diftance LM, they will be Diagonals; and:
where thofe Lines cut the extreme Rays FK and GK in the Points O, will be
marked out the Diminution of the Square, whereof FG is the Side ; and where
the fame Lines cut the Lines Z, Z, €@c. in the Points Q, Q, Ge. Parallels to
the Bafe Line are to be drawn, which will give the Diminution of all the Squares,
and the fame Number of Sidesas in the little Plan. And ftill, the more remote:
the Points of Diftance are from the Points of Sight, the more the Objects are di-
minifhed. Hence all the Beauty of a Perfpective depends on the nice Adjuftment
of the Interval between the Points of Diftance and that of Sight: On which Ac
count we have added a third Figure, witha Diverfity of Intervals, to evince the
Truth of whatis juft now obferved. Suppofe then R to be the Point of Sight,
andS StheExtreme Rays; if the Point of Diftance be at T, it will cut the Ray
S Rinthe Point V, which will give the Diminution of the Square, whereof SS
is a Side: But it would be ridiculous to fee a Square fo extravagantly deep from:
the Point of Diftance T, being fo much too near the Point of Sight R. In Effect,
the leaft, that is any-wife allowable, is for the Point of Diftance to be removed from
that of Sight, half the Breadth of the whole Draught or Perfpective; (fuch as
is the Diftance of X from R ;) by reafon fuch Removals always give a Right An-
gle at the Speétator’s Eye. It would, however, be ftill more agreeable at 1, the
Line in that Cafe cutting the Square at 2; and it would be better yet at 3, cut-
ting at 4; and beft of all at 5; being then remote enough, and making the Square:
fhorter at 6: The Reafon whereof will be affign’d under the following Figure.

It may be demanded, Why, throughout the Courfe of this Work, Ihave put
the Points of Diftance fo near, when they have fo much better Effect at a greater
Diftance? The Anfwer is, That the Book not being intended to be view’d
merely out of Curiofity, but to inftruct, it was neceffary every Circumftance
fhould be feen, that the Methods might be the better conceiv’d : For this Rea-
fon we have included as much of the feveral Operations as poffibly we might.

14

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PRACTICAL

PERSPECTIVE

Of the DisTANCE, or REMOVAL.

W Evhave already faid, in fpeaking of the vifual Rays, that the Eye cannot
commodioufly take in more than is included ina right Angle ; that is,

that the Sight does not receive Objects fully and diftinétly, when the vifual Rays

exceed a right Angle. The Reafon is, that the Pupil being nearly in the Center

of the Eye, does not well admit above a Quadrant of a Circle; fo that all the

Rays exceeding that, have only a dim confufed Effect, Onthis Accountir is bet-

ter tohavethe Angle lefs than greater ; for Inftance, two thirds of aright Angle,

or fixty Degrees, but not lefs, iby Reafon the Rays, in fuch Cafe, being fo ftrait-

ned, do not fatisfy the Eye, the Angle being little more than a Point in the Pu-

pil. To fhew this Difference in Figures : Suppofe the Plans and Squares the fame

__as in the laft Figure, the Diftance of the Point T from R will give the Diftance
‘of T from the terreftrial Line; where it would be neceffary the Angle fhould

open much farther, to fee the Extremes Y Y. If it only opened toa right Angle,

the Eye could not fee all; as T, for Inftance, could not fee beyond the Points.
V.V: Whence would arifea very faulty @erfpective, inafmuch as what fhould

exhibit a Square, will.now only forma Parallelogram. The neareft one can put

it is in the Point X, which, as we have already obferved, is the juft Meafure of
a right Angle, comprehending the whole Piece Y Y. If it be carried ftill farther

back from the Point of Sight, it will be ftill the more agreeable, as in I, where

the Angle will only be 72 Degrees: If it be brought ‘back as far as Z, it will

be in Perfection, inafmuch as the Rays being now the lefs dilated, have the

more Force, and exhibit Objeéts with the greater Vivacity. But I would never

choofe to go beyond five, for the Reafon already infinuated, that the Angle then

dwindles to a mere Point. Too much Care, then, cannot be taken in the Difpo-

fal of Points of fo much Importance; with Regard to which it muft be efteemed

a certain Rule, that the Diftance be equal to the Space between the dire&t Ray

and the Corner of the Perfpective. +R, for Inftance, is the direét Ray and

X —-L the leaft Diftance, whichis equal to-|- Y. This Meafure being taken,

mutt be fet off each Way from the Point of Sight, as here from R toSS; or only

one Way, asin the following Page.

Thus much we learn from Reafons that regard the Eye: But Experience. fur-
nifhes another noble Rule, which may be general too, provided it be ufed with
Difcretion, viz. That having chofe the Place where the Perfpective is to be
made, you are to determine from what Quarter it is to be feen to the beft Ad-
vantage ; then taking the Diftance from this Place to the firft, fet off this Inter-
val, by alittle Scale, from the Point of Sight to the Point of Diftance, provided
it be not tooremote : Which is a Circumftance that will require fome Difcretion,
to avoid the Inconveniences either of placing it too near, or coo far off.

#5

PRACTICAL

Se a NES RSC Ser hhc AP A sSNA hac seamen

ee Fe RS CS RE A

16 PERGPECTUVE
RARAARAARARRARARARRARAAARRRARRARARAAAR

ApvverT. I. Relating to the Side-Point.

7 ELE Rules for the Front Points, are never chang’d for the Points of the
Sides, as being both founded on the fame Caufe, which always produces
the like Effects: We fhall fpare therefore to fpeak particularly thereof, the
Praétice for Side Points being the fame as for thofe of the Front ; as is fhewn
in Fig. . where the terreftrial Line A B has the very fame Divifions as the pre-
ceding ones: And if the Point of Sight be fuppofed in C, and the Point of Di-
ftance in D, drawing the Line A D, you will have the InterfectionsQ, Q, ESc,
which give the Diminutions of the Squares in the fame Number as the former.
The reft will be learnt from the fucceeding Rules.

Apvervt. IL Of the Depths or Hollowings.

A Perspective may be funk as deep as one pleafes, by means of the ter-
reftrial Line, drawing Lines from that Line, as E F, to the Points of Diftance
H 1: for where they interfeét the vifual Rays E G and F G, in the Points K, K,
we have already obferv’d, the Diminutions of the firft.Square will be. Now, if
we take this Line K L for the terreftrial Line, and from its Extremes K K draw
Lines to the Points of Diftance; where thefe cut the fame Lines E Gand F G,
viz. in the Points LL, will be the Diminution of the fecond Square, which will
have as many Divifions and Squares as the firft. Again, if we take this Line
LL, and repeat the fame Operation, we fhall have the Diminution of the third
Square in the Point M: And if we begin again with this, we fhall have a fourth’s
and fo on, till we arrive at a Point, which will be a Length that will appear in-
finite. By fuch Means, then, ic is eafy finking and fhortning Per{pectives :
Thus, if you would have it twice its Width, proceed as already directed; and if
you would only have it half thereof, draw a Line where thofe from the Points
of Diftance interfeét each other, and you will have your Requett.

Since this is infallible, that as many vifwal Rays as cut the Diagonal Line,
drawn from the Points of Diitance to the terreftrial Line, fo many Squares of
Depths you have ; it follows, as has been already hinted, that you may give the
Perfpective what Depth you pleafe. For if, inftead of drawing the Diagonal from
the Ray F to the Point of Diftance O, you draw it from Q, you will want two
Squares of the other diminifh’d Square R and if you would have two Squares
more than the Square R, draw a Line from the fame Point O, cutting two Rays,
to'V: If you defire four, take X; if fix, Ys and if the entire Square, Z
Which is a wondrous Eafinefs, when well underftood.,

17 PERSPECTIVE

ApvertT. Ill. Of the Meafures upon the Bate.

Y the Bafe Line alone one may give any Depth, and in any Place, at Pleafure,

without the ufe of Squares; which is a very expeditious Way, tho’ fome-
what difficult to learn. We fhall, however, endeavour to make it underftood,
by Reafon we fhall make frequent ufe thereof. For an Example; Suppofe the
- Bafe Line, BS; the Pointof View A; and the Points of Diftance DE; if now
you would makea Plan of a Cube BC, draw two occult, or dotted Lines, from
the Extremes B C, tothe Points of Sight: Then, to givethe Breadth, take the
fame Meafure BC, and fet it off on the terreftrial Line C F; and from F draw a
Line to the Point of Diftance D ; and where this Line interfects the firft Ray C,
in the Point G, will be the Diminution of the Plan of the Cube BEI GC.
_ If you wouldhave an Objeét farther towards the Middle, take the Breadth and
the Diftance of the Bafe Line, as IK ; and to have the Depth, fet it as you
would have it on the fame Bafe, as LM, and its Width both on LM ; then from
L and M draw occult Lines to the Point of Diftance D, and from the Points NO,
where thofe Lines interfeét the Ray K, draw Parallels to the terreftrial Line, and
you will have the Square Q PON.

After the fame Manner may you fet off the other Side of the Square, which ©
fhould be on the Bafe ; as BH GC is here transferred to V. The Points M and
T, which are only two Feet from the Point S, afford a very narrow Figure in X,
as being very near.

AvvERT.IV. Of the Bafe Line, and a fingle Point of Diftance.

Src ez the Depths and Widths may be had by Means of this Bafe Line, we
need not give ourfelves any further Trouble in the making of Squares ; as fhall
be fhewn inthis Example. Suppofe a Row of Trees, or Columns, is to be made
on each Side; onthe Bafe Line lay down the Place, and the Diltance between
them, with their Breadth or Diameters, as ABCDEFG, then laying a Ruler
from the Point of Diftance O, to each of the Pointt ABCDEFG, the Inter-
fe&tions it makes on the vifual Ray AH, will be the Bounds of the Objeéts de-
fired. To fet them off on the other Side, upon the Ray GH; fet one Foot of
your Compaffes on the Point of the Eye Hy, and with the other ftrike an Arch:
The Point wherein this cuts the Ray G H, will be the correfponding Bound.
Thus M will be the fame with N, andfoof thereft; thro’ which drawing Paral-
lels, you will have the Breadths. And as for the Length, make it at Pleafure ;
fetting it off from A, for Inftance, to P, and then from P drawing a Line to
H; and where this cuts the other Parallels, will be formed the Plan required:
Which you may make either round or fquare.

ApveRT. V. Not to deceive one’s [elf in the Meafures.

NEVER put any Objects that are intended to be within the Plan, on the Side
of the Point of Diftance, where you are to draw Lines for managing the Depth.
Thus, fuppofe AB the vifual Ray whereon the Meafures are to be marked ; if
you. would produce the Points C and D thro’ the fame, don’t draw the Lineg
from the Point of Diftance E, but from that oppofite thereto, F: Or if C and
D were onthe Infide, as Gand H are, you fhould not draw from the Point F
but from E ; by Reafon the Line of Interfection is found between the two. Con-
fequently, the two will cut each other in the fame Points I, K. 3

CT 5 AE CN ie ae tse my man.

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Pp 5

18 PERAS PEC TIVE

Apvert. VI. Of a fingle Point of Diftance.

”A PERSON is fometimes fo ftreightned for want of Room, either on a
L-\ Wall, a Cloth, Paper, or the like, that it is impoffible to make above one
Point of Diftance: On which Occafion, fuch as have been always accuftomed to
two. findthemfelves at a Lofs. This we are now to recover them from, and to
give them to underftand how a fingle Point fuffices for the Bufinefs. Suppofe,
then, we have a Pavement to make of fquare Stones, and that we have already
drawn all the vifual Rays to the Point A; to get the Diminutions of which, we
have Lines to draw to the Points of Diftance, the Interfections whereof are to
give us Points for Parallels to be drawn through: But here being only one, viz.
B, draw the fingle diagonal Stroke CB, to cut all the vifual Rays. And, to
mark the fame Interfeétions on the oppofite Rays, forthe drawing of Parallels ;
fet, as already direéted, one Foot of your Compafies in the Point A, and fweep
the other through all the Interfections, as IP. This however is only advifeable
for what is to be viewed in Front; another Method is to be given for what is to
be feen Side-wife; thus: Set one Foot of your Compafies on the Bafe Line, and
with the other take the Interfe€tion you want to transfer, as D, and fet it upon the
PerpendicularO E, marking the Extent thereof, as F ; then draw a Line from
Dto F, and you will have the fame as if there had been two Points of Diftance.
And fo of all the other Interfections.

ADVERT. VII. How to do without making Ufe of the Diagonal.

IF one would ufe the extreme Ray GH for the Line of Interfection, the Ob-
jects K LLM NO mutt be fet on the Bafe Line, and from them Lines are to be
drawn tothe Point of Diftance I; which is here to be removed as far as poffible,
that the Diminution of the Perfpective may have the better Effeét: (For if that
Point were too near the Point of Sight G, the Objects would be too flat; I mean,
for Example, that a Square would appear a Parallelogram.) Then from the
Point I draw Lines to the feveral Objects K L MNO, and mark the Interfections
thereof on the Ray GH, and through thefe Interfections draw Parallels to the
terreftrial Line, as here PQ, &c. This Method is not much in ufe, tho’ fome
fet a Value on it.

ApvervT. VII. Of feveral Ways of Shortning or Diminifhing.

IF you chance to be ftreightned, and cannot remove the Point of Diftance
far enough ; from the Foot of the Ray RS erect a Perpendicular TS, which will
receive the Interfections, and give a greater Diminution: And if you would have
the Diminutions ftill more, draw a flope Line, as X, which, by Means of its In-
clination, will give the Interfections ftill clofer: Then, to draw the Parallels, you
_ have nothing to do but fet off the Line X or T on the Foot of the Ray, asin V ;
and from thofe Points draw Parallels to the terreftrial Line.

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PERSPECTIVE

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19 PERSPECTIVE

Of Planes view'’d directly, or in Front.

FE ROM Advert. III. and IV. as well as fromthe Elevations that follow 3 it
will appear that our Intention is not to ufe geometrical Plans, in order to the
drawing of Perfpeétives: That being a double Labour ; and there being fcarce.
any Painter would give himfelf the Trouble, feeing 1 teach him to do the fame
Thing, by the ufe of the terreftrial Line. But, as there is no Rule fo general,
but has its Exception ; fo there are certain Figures which cannot be put in Per-
fpeétive withour the ufe of fuch Plans: Befide, the Confufion a Man would be
under, fhoulda Plane be given him to put in Perfpective, if he had not been in-
ftruéted how to proceed. On fuch Confiderations, I have been induc’d to give
the following Rules; which may fuffice to fhew how any Plane that can be re-
quir’d, or even imagin’d, may be put in Perfpective.

1. To foorten, or diminifh a Square;as ABCD: From A and B, to the Point.
of Sight E, draw the Lines A E, B E; and from the fame Angles A and B,
draw two Diagonals FB, AG; and the Points H and I, where they interfect
the Rays A Eand BE, will give the Square ABCD, diminifh’'d in AHIB.
To do it without the geometrical Plan; draw a Line from B to F,- or from A
to G ; or fet off the Line A B on the terreftrial Line; asim BK: and from K
draw another Line to F ; which will give the fame InterfectionI, on the Ray BE.

2. To diminifh a Square view'd by the Angle D: Having defcrib’d the Plan A B
C D, draw a Line to touch or rafe the Angle B, and falling perpendicularly on
BD. This being continued as a Bafe-Line, lay your Ruler on the Sides of the
Square A D.and DC; and where the Ruler cuts the terreftrial Line, make Points,
Fil. Then from H and B draw“Lines to the Pointsof Diftance P ; and from
I draw a Line to the other Point of Diftance Gs and in the Interfections of
thofe Lines make Points, which will give you the Square KLMB. Todo
without the Plan: Set off the Diameter each way from the middle Point B ; as,
to Hand I. But in either Cafeno Line is to be drawn to the Point of Sight, O.

3. To diminifo a Circle: Draw a Square ABC D about it; and from the An-
gles A Dand C B draw Diagonals, dividing the Circle into eight Parts; and thro’
the Points where they cut it, OO, draw Lines from the Bafe-Line, perpendi-
cularto DEF. Thendraw two DiagonalsQ RSP, interfeting each other at
right Angles in the Centre G. The Plan thus difpos’d; from all the Perpendi-
culars draw Lines to the Point of Sight H; and where they are interfected by the
Diagonals A K, and BI, make Points; the two laft of which, MN, give the
Square, which is to be divided into four by Diagonals, interfeéting each other, in
the Point P. Laftly, from the Extremes of this Crofs, draw curve Lines. thro’
the faid Points, which will give the Form of the Circle in Perfpective. This Me-
thod may ferve for fmall Circles; but for large ones we fhall give another Me-
thod, more exact.

4. This Figure is a Compound of the two firft ; which 1s all we need to fay
about it.

5. This too depends on the two firft; only here isa Lift, or Border, going round,
which the othershave not. To put the Lift in Perfpective: From the four Rays
ABCD draw Lines from the Point of Sight G; and where the inner Rays
BC interfeét the Diagonals DF and DE, draw Parallels to the Bafe-Line ; and
you will have your Defire.

The fixth is the fame as the fecond; except that it is furrounded with two Borders.

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20 PERSPECTIVE

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Prawns viewd obliquely, or fide-wife.

T HESE Plans being much the fame with
thofé already difpatch’d, are to be manag’d
after the fame manner. In Effect, it would be
lofing Time to repeat how they are to be dimi-
nifh’d in Perfpective; a bare Infpection of the,
Figure fufficing to thew, that all the Difference
between thefe and the former confifts in the Si-
tuation of the Objects, which are here {hewn la-
terally, and there in front.

All the A A A’s are Points of Sight, and the
BBB’s Points of Diftance. ‘

PRACT IC A EL.

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Of a TRIANGLE.

RIAN GLE 5S, according to the Order of Numbers, ought to
precede Squares; but, according to Reafon, they are to come after
them in this Work, as being more difficult to put in Perfpective: Not
on account of the Plan, which is eafy enough, as only confifting of
three Lines join’d together, but on account of the Obliquity of its Sides.
We now come to apply fome of the Advertifements, relating to the
Meafures on the Bafe-Line AB: For, to put this Triangle in Perfpec-
tive, from all the Angles thereof, 1, 2 and 3, Perpendiculars are to be
drawn to AB. Then fetting one Foot of your Compafies in the Inter-
fe&tions, with the other fet off the Diftances of the Parts of the Object
from the terreftrial Line, along the fame Line, by ftriking Arches, as.
from 2 to 2, from 3 to 3, &c. This done, having drawn another Bafe-
Line in another Place, as hereunder E F, transfer the Meafures from
A Bto EF, and to the Point of Sight C draw Lines from the Points.
I, 2, 3, @vc. Laftly, having pitch’d one Point of Diftance D, draw
Lines thereto from the other Points of Depth, 1, 2, 3, &c. And be-
tween the InterfeCtions made by thefe with the vifual Rays, Lines being
drawn, will give the Triangle requir’d.

If you would give it the Lift or Breadth, repeat the fame over again
for the feveral Points thereof; only ufing other Figures to prevent Con-
fufion ; as, next to 1, 43; next 2; 5; 3, 6, &c. Then drawing Perpen-
diculars to the Point C, and between the Points, where they interfect the
others, draw Lines as you fee in the Scheme.

The Equilateral Triangle, fuch as that here defcribed, is infcribed in
a Circle, 7..¢,.a Circle may be drawn upon it, every Side fubtending 120,
Degrees. | 3,

PRACTICAL

22

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Of the PENTAGON, or Five-Angke.

Th HE way to conftrué a Pentagon is to defcribe a Circle,
and divide it into five equal Parts, of feventy-two De-
grees each; then, for putting it in Perfpedctive, the Method is
the fame as for the Triangle, as appears from the Figure :
Where, however, it isobfervable, that there isa Lift or Breadth,
whereas it is only laid down, on the Bafe Line, fingle; the
Reader being fuppos'd fufficiently inftru@ted in what relates to
the Lift, from the Triangle. The Point of Sight, both of the
Front and the Side, is A; the Point of Diftance B ; the vifual
Rays, which are the Perpendiculars drawn from the Angles of
the Plan to the Bafe Line, are drawn tothe Point of Sight A;
and the other Rays that give the Diminution, and the Place of
the Angles, to the Point of Diftance B. As_ 2 cuts the Ray
mark’d 2, which gives the Angle 2, 4 gives the Angle 4;
and fo of the reft. All the reft is clear enough; regard,
however, is to be had to one Thing, that all the Angles tend
towards the Center 6: For this Reafon the Centre is to be
mark’d in the Plans in Perfpedtive, as well as in the geome-
trical Plans,

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Of th Hex acon, or Six-Angle.

HE Hexacon is aPlane with fix Angles, and as many Sides ;
tis the eafieft to defcribe of all the Polygons, by reafon the fame
Aperture of the Compaffes, that 1s, the Radius wherewith its Circle is
defcribed, gives its Sides of 60 Degrees apiece. As to the -putting ic in
Perfpective, the Method does not at all differ from that of the Triangle,
or Pentagon ; either when fingle, or with the Lift or Thicknefs, A is the
Point of Sight, and B that of Diftance. |
Since we have a good deal of room in this Page, we think it not
amifs to give a little Method of putting the Lifts or Thickneffes of all
Polygons, regular or irregular, in Perfpective: And the prefent Hexa-
gon fhall ferve for an Example of our Propofition. Suppofe the Front
Plan of Fig. 3. to be only a fingle Stroke, and it were requir'd to give
it a Lift or Thicknefs all around: To do this in Perfpective, lay your
Ruler along the fingle Sides, and make Points in the Horizon where
it cuts the fame; thus laying it along the Side AB, it will cut the Ho-
rizon in C; then laying it along B D, it will give the Point E; and
the like of the other Sides. Before you proceed any farther, draw occult
Lines from the feveral Angles through the Center F, which Lines are
to receive the Interfections that give the Diminutions. Such Difpofitions
made, fet the Breadth of the Band or Lift on the Bafe-Line, as AH, and
draw the firft Breadth to the Point of Diftance G, and where the Line
G H cuts I, will be the Bound of the Thicknefs of the firft Side, which
is to determine for all the reft : For from this Point a Line is to be
drawn to the Point correfponding to this Side C, and the Interfection of
this Line with K will give the Diminution; from the Point whereof draw-
ing a Line to the Point E, correfponding to the Line BD, you will have
the Diminution for the Point L, which ferves for the laft Side L M:
Then transferring all the fame Meafures to the other Side, you will have
the Figure complete. : |
Hereafter we fhall have occafion to give another Method.

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24 PERSPECTIVE

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Of th HErPtTAGON, or Sept-Angle.

H E Hepracon is formed within a Circle, as the other Poly-

gons are; in order to which the Circle is divided into feven Parts,
each Side fubtending 51 Deg. 25 Min and fometimes more. The Me-
thod of putting itin Perfpeétive is the fame with that of the preceding
ones, as to the Perpendiculars falling from the Angles to the Bafe-Line,
which are all drawn to the Point of View A; but as to the Diminu-
tion, and the Lines that give the Points of the Angles, it is different,
and rather according to tHe feventh Advertifement, though we donot ab-
folutely approve that, as thinking the eighth Advertifement the better.
But to condefcend to fuch as do ufe it, and fhew them that it does not
diminifh enough. :

Having drawn Perpendiculars from the Angles of the Plan to the ter-
reftrial Line, as in the preceding Cafes, a Perpendicular is to be made on
one Side, as A B, to receive the Interfeétions of the Parallels drawn
through all the Angles. Thus, the firft Angle being plac’d on the ter-
reftrial Line of 2 and 7, I drawa Parallel through both, cutting the Per-
pendicular in C, After the fame manner, the Angles 3 and 6 give the In-
terfection D, and 4 5 the Interfection E. This Line A B, thus divided,
mutt be fet off on the Bafe-Line of the Plan to be diminifh’d, begin-
ning to put the Point B inF, as in the Figure. Then making the other
Divifions CDE, and from thefe drawing Lines to the Point of Diftance
O, from the Interfections of the extreme Ray draw Parallels to the ter-
reftrial Line, and where thefe cut the Rays that bear the Numbers of the
Angles, Points are to be made, which, being join’d by Right Lines,
will give the Figure defir’d. As to the Thicknefs, or “Lift, ’tis to be
made after one of thé preceding Manners. 4,

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25 PERSPECTIVE

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Of the Octocon, or Eight-Angle.

¥ H E O&togon is form’d of a Circle, divided
into eight Parts, of forty five Degrees each,
the Divifions whereof, Lines -being drawn, will
form an Odtogon, that is, a Figure of eight An-
gles, and as many Sides. ‘The Rules already de-
liver’d, fhew abundantly how it is to be put in Per-
{pective, whether for a Front ora Side View. I
{hall only obferve here, that the Front-Plan 1s to
be diminifhed according to 4dvert. VIII. and the
Side-Plan according to the VIIth. The Point of
View is A, and that of Diftance B. The reft is

too obvious to need an Explanation.

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26 PERSPECT FTVE

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2

Another Method for the OC TO GON.

T HI 1S Method of conduéting the Oc To GON was invented by Sertzo.
The Praétice is thus; having found aSquare A BCD the ordinary
Way, divide the Bafe-Line C D into ten Parts, and, leaving three on each
Hand; from the third of either Side E and F, draw Lines to the Points of
Sight, G, and through the Interfections of thofe Lines with the Diagonals
© O, draw Parallels to the terreftrial Line, cutting the Sides of the
Square in the Points H I K L: Then joining the Points EH, IE, F K,
LF, by Lines, you will have an Octogon, as in the preceding Figure.

Of th HExacGon, or Six-Angle.

Ei E fame Serlio has contriv’d a like Way of managing the Hex-
AGoN. Suppofe, as above, a Square ABCD, and the Bafe-Line
AD divided into four Parts, from one of which, on either Side E and F,
draw Lines to the Point of Sight H; then through the Interfection of the
Diagonals, which is the Middle of the Square G, draw a Parallel to the
Bafe-Line, cutting the Sides of the Square in 1K; laftly, drawing Lines
through thefe Points EIE, and F KF, there will be found a Hexagon.
I thall fay nothing of the Octogon view'd fide-wife ; fince, as has been
fo often repeated, the Method is the fame as for that view’d in front.

PRACTICAL ae |

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2” PERSPECTIVE

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06 & MBHOCSO

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Of the Double Oc ToGoN.

C\ UPPOSING a fingle O&ogon already made, if ’tis re-
quired to have it double, or to give ita Thicknels, or Lift,

proceed thus : Set the Breadth or Thicknefs you are willing to
give it, within the Square comprehending the Octogon, as here
AB; and from thefe Points draw Lines to the Point of Sight
C; and where thefe Lines cut the Diagonals, as in OO, draw
Parallels DD, which will form a Sort of Band round the
Square ; laftly, draw occult Lines from Angle to Angle, inter-
fecting each other in N; and where they cut the Lines of the
inner Square, viz. in the Points EF GHIKLM, will be the
Bounds of the inner O¢togon.

a SESSSSEERSES 2 SEERESESRS 2 SESSSae SESE EBSO DED LEOS~
Of the Double HE XA GON.

HE fame may be done with a Hexagon drawn in a
a Square. It would be needlefs to repeat Particulars, fince
the Figure will clear any Doubts that may arife.

The Oéogon view’d Side-wife, is managed precifely as that
viewed in Front; the Point of Sight is A, and that of Dif-
tance B.

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PRACTICAL

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Of the CIRCLE.

| HE more Sides a Polygon has, the fooner and the

eafier is it converted into a Circle. For thisreafon Serlio
dire4ts a Semi-circle to be drawn, and the Circumference there-
of to be divided into any number of equal Parts at Pleafure;
for the more Divifions, the more perfect the Rotundity: Thus
the Semi-circle A Z B is here divided into eight Parts, which
give fixteen for the whole Circle ; then from the feveral Divi-
fions Z Z, &c. Perpendiculars are rais‘d to the Bafe Line in
the Points E E, &c. this done, the two Diagonals are to be
drawn to the Points of Diftance, which are here remov'd be-
yond the Compals of the Plate, but which are to be fupposd,.
as ufual, in the Horizon: ‘Thus you get a Square AHIB. And
this Square thus form’d, draw Lines from all the Points E to-
wards the Point of Sight, as far as the Line HI, and thro’ the
InterfeG@ions of thofe Lines draw Parallels; then, beginning
in the Middle of one of the Sides of the Square to makea
Point, as a, and another Point 4 in the oppofite Angle, as if
you were about to draw a Diagonal; and proceeding thus to
make Points from Angle to Angle, according to the Direction
of Diagonals, as a bcdefghikimnopg, thefe Points will
form a perfect Rotundity ; fo that connecting them together
by crooked or circular Lines drawn by the Hand, you will
have your Circle in Perfpective. “Tis neceffary People who
deal in Perfpective have this Rule of diminifhing Circles very
familiar to them, by reafon of the frequent Ufe thereof in
Columns, Vaults, Arches, Apertures of Doors, Windows, Ee,

PRACTICAL, a8

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29 PERSPECTIVE

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Of the Double CIRCLE.

HE firft Circle is fuppofed the fame that we have juft
now been defcribing ; and ’tis requird to give it a Thick-
nefs,or Lift, by making another within-fide thereof : Thus, give
it any Breadth at Pleafure, as A C, and fromthe Center of the
outer Semi-circle G, defcribe the inner Semi-circle C D, which
you are farther to divide, like the great one, by drawing occult
Lines from the Divifions of the great one to the Center thereof:
and from the Interfe@ions of thofe Lines with the inner Circle,
draw Perpendiculars II, 11, @e. to the Bafe-Line; and, to
prevent Confufion, let thefe laft Lines be dotted. This done,
from the Points-I of the Bafe-Line draw dotted Lines towards.
the Point of Sight F, as far asthe Line H K, and through their
Interfe€tions, with the Diagonals draw other dotted Lines MN,
which will give the Thicknefs (G Q)the Circle is to have.
Laftly, draw Lines from all the Angles of the great Circle to-
wards the Center, and the Points wherein they interfec the
dotted Lines abcdefghikimnopg will be the Points,
which, conneéted with curve Lines, will form the inner Cir-
cle’s Circumference. 7
A Perfon who fhould defire a Plan of three, four, five, or
fix Circles in Perfpeétive, muft lay them all down in the geo-
metrical Plan after the fame manner asthe fecond is done in
this Example. 3

PRACTICAL 29

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no PRRSPECTIVE

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SHIN Loe és Ane SD MS Y \e REX BONS eK ‘<e) MADAM AUS AE CR Ke ee eK ‘i 2 A

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APwuan of a Square view'd Angle-wife.

I F it fhould be required to draw a Square view'd by an Angle
§. dire&tly oppofite tothe Eye, there is nothing more requir ‘d
than to follow the Rule already laid down; which is, to
double the Diameter A B upon the Bafe Line, as here in A C,
and from the Points A and C to draw two Lines to the Point
of Diftance D, then to fet off the Meafures of the Line A Con
the Bafe Line towards A E, and from E A to draw Lines to
the Point of Diftance F, then will the three Interfe€tions of the
Lines H1K be the Bounds of the Square defired, AIH K,

When fuch a Plan isto be divided into feveral Parts, lay down
the Number of Divifions required between the Points Cand A,
and the fame Number on the other fide AE; and from a all
thefe Points draw Lines to the Points of Diftance: As in the
prefent Figure, which has eight Squares on each pies and
fixty-four in all.

€ in the fame Plan, thus view’d by the Angle, it were only
required to have four little Plans in the four Corners, as four
Lodges, Columns, Trees, or the like Objects, fet the Width
thereof on the Bafe Line, within theSideof the Square A B or
AC, Dand Ebeing between AB, and FG betweenAC; from
which Points drawing Lines to the Points of Diflance H I,
their Interfections will give the four Plans K LM N required.

PRACTICAL

gt PERSPECTIVE

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AG, SG SAAS EE I SL OS
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PEGE AAB MSDE SEG

A Pavement of SQUARES viewed by the Angles.

| og petted we areabout Places viewed angle-wife, it may not be amifs to fhew
how a Pavement of a Hall, Church, or other Place is to be conducted.
Having drawn the Horizon parallel to the terreftrial Line AB, the Point of Sight
€, and the Points of Diftance D and E, divide the Bafe into as many Parts as
you would have Squares; then draw Lines from the Extremities thereof A and B,
to the Point of SightC, and from the fame Points A and B draw two Diagonals
to the Points of Diftance D E, the Points of Interfeétion FG will give the Square
f the Hall, and through them the Line of Depth HI is to be drawn ; then
@raw Lines from all the Divifions of the Bafe Line to the Point of Diftance D
and E, and between the Rays A B you will have your Defire; as appears from
the Figure. But here arifes a Difficulty, viz. how to fill the vacant Space BB
and GI, AA and HF, with the fame Squares ; for ’tis fuppos’d the Bafe Line
‘cannot be prolonged any farther. On fuch Occafion, take the Meafure of one of
the Squares, as GK, on the Line FG, and fet it off on the fame Line HI as
‘fen as twill go, and you will have the Points LMNOPQ and R, through
which drawing Lines to the Point of Diftance, you will have the fame Squares as
‘before ; fuch are thofe here marked with Dots. The fame Method of fetting
‘fF the Meafures on the Line of Depth, will be exemplified in other Pavements .
. ‘ereafter.

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OFS QUAREs encompaffed with a Lalt, or Fillet.

HIE Method of managing this fecond Pavement with a Band around it, is
: the fame with that of fingle Squares viewed in Front; we fhall therefore
decline to wafte any Time in teaching it, fince we have already given fo many Fi-
gures thereof. It may be proper, however, to add, that the Bafe Line is to be
‘divided into unequal Parts, as A, B and C, and Lines to be drawn from all thefe
Divifions to the Point of SightD, and through the Points where thefe are inter-
fe€ted by the Diagonals AE, and GF, Parallels to the Bafe Line are to be
drawn ; as in the Figure.

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32 PERSPECTIVE
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Pavements view’d Angle-wife, encompafsd with a
Band or Fillet. ;

OR fuch kind of Pavement, the Bafe Line AB is to
be divided into unequal Parts, the largeft whereof are
to be for the Squares, and the {maller for the Band or Fillet ;
and from all thefe Divifions, Lines are to be drawn to the Points
of Diftance EF: As has been already directed in fingle Squares,

nd tnh eS REED BEB

Pavements of Squares wewd im Front, encom-
pafs'd with Lifts, or Bands, whofe Squares are
divided by the Angle.

OR this fifth kind of Pavement the fame Method is to be

taken as in the fecond, by dividing the Bafe Line into
unequal Parts; but to make the Square that is feen Angle-wile
in the Middle, the largeft is to be divided into two, as ABC.
DEFG; from the feveral Points whereof, Lines are to be
drawn to the Points of Diftance, the Interfe€tions whereof
Will give the Square, orLozange, in the Middle.

oa 3

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PR AG T EGA LE;

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33 PER SPECO TIVE
BIG 2G 1G 26 2 2G 1 0G 1G 3G BE BE IC 1G BS 1S 1 EI NE Be EE 1S

Pavement of Squares view’d Angle-wife, with
Chains of Squares zz Front.

E fuppofe the Perfpective, or Diminution of the

_ Square, by drawing the Line of Depth, to be already

done, that we may fave the Trouble of too frequent Repetiti-
ons in the enfuing Pavements.

To manage this fixth Sort of Pavement, divide the Bafe
‘Line into equal Parts, and from fome of them, as ABC, draw
Lines directly tothe Point of Sight, and from all the reftdraw
Lines to the Point of Diftance, but without marking them
thro’ the Chains. After all fuch as are thus view d by the An-
gle are thus drawn, Parallels muft be drawn for the reft,
meeting the Angles of the former; ex. gr. From the Angle D
and E the Line F to be drawn, and of all the reft, as is {hewn
by the Figure: Care ftill to be taken, that there be always the
fame Number of Squares between the Chains; as here we
have three between AB.

Pavement of Squares 7” Front, with Chains of
et: Squares Angle-wife. 3

" HIS feventh Sort of Pavement is perform’d much:after
. the Manner of the preceding, by dividing the Bafe Line
into equal Parts, and fromthe Divifions drawing Lines to the
Point of Sight, to form the Bands or Chains GH1; yet there is
fomewhat more in it, Care being required to make the crofs
Chains of the fame Breadth asthe others that tend to the Point
of Sight O, and that there be the fame Number of Squares be-
tween the Vacuities, The reftis obvious enough, z

33

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34 PERSPECTIVE

C4B3}OCDOKRHOCO EB COKBY COOKBYODOKBYOCONGY

+. ces PeeeEeenre eer ce

OCSOKBRAMNOTDI OAR AOD Me WOOK te Ke ROCOa aE

Pavement of Ottogons itermix’d with Squares.

E fhould never have done, were we to give all the Va-
rieties of Pavements; a Perfon of Fancy that Way
would eafily invent an Infinity. ‘This feventh Way is‘obvious
enough; all we add it for, is, to open the Mind, and furnith
Occafion for the contriving of others. All that is required is
to divide the Bafe Line into a Number of Parts, whereof the
Squares are to be formed, as already directed : Of hich Squares
a certain Number is to be taken, as here nine, five whereof
are full, and the reft only Halves; the full ones give the Infide
of the Figure 1 2 34 5, and the Diagonals of the reft,

6 7 89, give the Sides: The reft is evident.

Pavement of fingle Squares. wew'd in Front.

i og HIS FormI have put the laft, not as being the moft dif-:
ficult, for in Reality it is the eafieft of all, and the very
Beginning of Perfpective, but to intimate that itis the moft
ufeful and neceffary, the reft being feldom added but by Way
of Ornament,. and this ferving as the Foundation whereon any
oe is to be rais'd, to be made appear: As will be fhewn here-
after.

PRACTICAL 34

35 PER SPIE OT Live

Ah bab ANd eA atd h Aad nba t Abb tht PABP RAAB A Gd
6 CIE IESG ISR TOES
BEC UR EG UC UG EC OG RCL

everveveverrcy rrr trite rrr rT re

Plan of a GARDEN in Per fpeciive.

HAT we have been obferving, is confirmed by this

Plan: For, drawing Lines from allthe Divifions on

the Bafe Line to the Point of Sight, the Diagonals will give the
Depth of the whole Plan, and the Diminution of all the little
Squares, Laftly, fetting off the Alleys, Figures, &c. from the
correfpondent Quantities in the geometrical Plan, the whole
Parterre will be found in Perfpedtive ; as is {hewn in the Figure.
Let the Plan given you to diminifh, and put in Perfpective,

be of what Sort foever, the readieft Way will ftill be, todraw
a Square about it, and divide that into feveral lefler Squares.
For putting the grand Square, with all the leffer ones, in Per-
{pective, by the ordinary Rules, you have nothing farther to
do, but take Care that every Thing take up the fame Number
of little Squares in the diminifh’d Plan as in the geometrical
one, and the Figure of the one will be found in the other.

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36 PERSPECTIVE

TR BO eo 8) se SAB x Bh, SOB ever oe OB ne
IRAE ANNAN SRE NOU NS NSOR AEA
Surges RGgag = Noe BM BBap™ Meee” GIN Oi

PLAN of @ BurLpDINn Gin Perfpective.

“NERLIO, in his Treatife of Perspective, fets a

J great value on this Method of putting Plans in Perfpective,
asa Thing of fingular Ufe in Architecture, whereby a Perfon
is enabled to fhew one Part of a Building raisd, and the
reftin Platform ; but his Method for Buildings being the fame _
with that we have already laid down fora Garden, we need
not fay any Thing farther thereof: ‘The Figure is fufficient for
the reft. And from this one Figure Meafures are eafily taken
for any other, either more eafy or difficult ones.

In the fecond Part of this Treatife you fhall have a Me-
thod of reprefenting a whole Houfe in Perfpective, with all
the Members and Apartments thereof, from the Roof to the
Cellar. 2

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Plan of aCHURC Hy, in Perfpettive.

a. HIS Plan is conduéted according to Apverr. VII.
That is, all the Sides perpendicular to the BafeLine, as
are here the Places of the Walls and Pilafters, are drawn tothe
Bafe Line, and from that Line to the Point of Sight; and all
the other Sides parallel to the Bafe Line, as are here the
Breadths, &c. drawn toa Line on one Side, O P, which thus
fhews the Pointsa bcdefghik/. Thefe Points transferred
hence upon the Pafe Line asa 4, &c. and-Lines drawn from
them to the Points of Diftance, their InterfeGtions with the
extreme Ray, give Points for drawing Parallels through, ex-
hibiting the Diminution of every Thing: As fhewn by
a; 6, 6, hee. A
This Method of diminifhing on the extreme Ray is practis’d
by many ; and yet fuch as would take my Advice, fhould let
it alone, and rather follow the Method direéted in Apvert.VIIL
where a Perpendicular is rais'd on the End of the Bafe to re-
ceive the Interfections, and to obviate the Defect of the pre-
fent Method, which does not diminifh enough, unlefs where
the Points of Diftance are very remote: For in that Cafe, the
Effea is the fame as in the other Methods, |

*

PRACTICAL

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Pranof aHoule —_ a Garden.

H E Method of putting this Plan in Per-

fpective, is the fame with that of the Gar-
den alone ; fo that what is there faid may fuffice
for both. Our Defign in putting it here, is, to
fhew, that one may diminifh all Sorts of Plans,
whether confifting of equal or unequal Parts.

PRIA TC AL

a a I a

eR GREE A PRR IN ETP RUE IOI g Qh NR Si ae Nn PI

39 PERSPECTIVE

: ic og PIL Ce DEA Coed a Ce CEE : SO;
OE ay ae) OT OIE OM LO,

SHSGISCO SSI SSIS S SSSVSSs Gae SOHsoesogegseoes

Plan of aForRTIFICATION, im Perfpective.

O put a ForTIFICATION, or other Thing of the like

Kind in Perfpective, the Vith and VIlIth Apvert. are
to beus’d. The fame in Effe@ is the Method already laid
down for the Cuurcuand Houstg, viz. by drawing Perpen-
diculars fromall the Angles to the Bafe Line, and Rays from
the Bafe Line to the Point of Sight, and from the fame Angles
drawing Parallels tothe terreftrial Line, and marking the Di-
vifionson a Side-line, AB. Thefe Divifions being transferr'd
thence to the Bafe Line, and Lines drawn from them to the
Point of Diftance, we fhall have the Line of InterfeCtionsC D.
But by Reafon we have not Room here to put it on the Bafe
Line we have added it underneath the Figure, asin AB. Laft-
ly, having fix’d the Point of DiftanceinE; draw Lines thence
to all the Divifions of AB, cutting the Line of Interfection
CD in fo many Parts; which Line, CD, with its Divifions,
is to be transferr’d to the Bottom of theextreme Ray, or atleaft
fet on each Side, as DD ; and from all the Pointsof the Line
DC, draw Parallels, or only Mock-points, on the Ray pro-
ceeding from the Angle of the Plan belonging thereto. Which
Points, connected by Lines, give the Figure required.

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4,0 PERSPECTIVE

EP TC IH ESI PASI
FG Fe SFY EG FR IR EG
a ARRAS 0S ANOS TOS IOS TGS CAS OSS ONT ASOSOSTIS STONE OES DOSEN NESS

An Irregular Plan and Figure in Per-
an fpective.

Man who can perform what is directed un-

der the laft Article, will find no Difficulty
inany Thing elfe ; that being the moft intricate
of all Kinds of Plans in Perfpective. It was
judg’d, however, proper to add fome irregular
Thing, that might appear at firft Sight to be Dif-
ficult, in order to fhew that there 1s nothing but
what may be diminifh’d, in what View or Afpect

foever it be.

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oP et eNO LT ea ak an

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Another Plan of a CHURCH, iw Perfpective.

HE Manner of this Perfpective fhould feem very dif-

ferent from what we have hitherto delivered, by Reafon
of the different Difpofition ; but that we own ita Thies done
defignedly, to fhew that there are divers Ways and Manners,
tho’ all reducible to one. For this, in Effe@, is the fame
with what we havealready pretenibed for Fortifications, irregu-
lar Figures, and other Plans, with this Difference, that the
Parallels to the Bafe Line are there mark’d ona Side Line, and
here, ona Line in the Middle of the Plan: But the fame Ef-
fect is had from each Method; for drawing Lines from all the
Divifions of the middle Line to the Eye A, you will have the
Line of InterfeGtion BC, which is upon wa may be called
the Bafe Line DE.

To put it in Perfpe@tive, transfer the whole Length of the
terreftrial Line DEtoany Place at Pleafure, as DE, and fetoft
the Height of the Eye AF; then, putting the Line of Inter-
- feé&tion BC either in the Middle, or one Side, draw Parallels
to the Bafe Line thro’ all the Divifions to the extreme Rays.
DA, EA, and fetthe Breadth of the PilaftersD K on the Bafe
Line; then drawing a Line from K to the Point of Sight
A, the Points wherein it interfects the parallel Lines will be the
Widths of the Pilafters.

PRACTICAL

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ERRAIREREDeAe MESSRS

i. 2 Se
FOR
ELEVATIONS.
PICEA DER GRE S Aa Ges

a4 PER SPEC TING

SQV LS CHIEN C28 AER GOR9
x sho ws ft x B Re x us se OS Rid x a 3 AS.

Boe eo re a i On ie Oe te ete es
BSG MBAS IER BH ADS KERRI KH GDS MSH MEE MBO RG

Preliminary Inftructions neceljary tothe following Methods,

E fancy. the Reader is by this Time fufficiently. inftru@ed in whag
- relates-to-Ichnography and Planigraphy, confidered as.the Founda-
tions of Orthography and Scenography.

Orthography, we have already defined, the Elevation of the Face or
Front, &c. and Scenography the Elevation of the Whole, Seethe Deri,
NitroNnsat the Beginning of the Work.

To make myfelf more intelligible to fuch as are not verfed in the Ufe
of thofe. Words, we.purpofe for the future to call Ichnography, the Plan ;
the Orthography, the Upright, or Elevation af the Front; and Scenogra-
phy, the Elevation of the Whale.

‘Before we proceed any farther, it is to.be obferved, that Elevations ne.
ver give the Eye all che Angles of’ the Plan, and that the Quantity of Sides,
or Angles, depends on the Afpect or View the Object is taken in ; Thus, if
it be viewed in Front, as the Figure A, it will only fhew one Side, tho’
the Plan haye four; if ic be viewed' by the Angle, it will thew two, as Bg
but nevery more, in, whatever View it be. takeny’ We fpeak of Squares
for as to Objects of many Sides, they may fhew three, four, five, and more,

Now Objects declining ever fo little from the Point of View, are feen
by the Angle, and of Confequence muft fhew two Sides; And ftill the
farther they are removed from the Point of Sight, the more of themfelves
gd aes thus K E thews more of itfelf than CL, tho' cheir Thicknefg
be equal.

Rinther Thing to be obferved farther is, that what is parallel to the
Horizon when the Object is viewed in Front, asC DEF of the Door in
Fig, 1, becomes a vifual Ray when the fame Object is view'da little obs
liquely ; Thus CDEF, which in the upper Figure ftands in Front, becomes
a vifual Ray in that underneath, And, on the contrary, what isa Ray in —
the upper, becomes parallel to the Bafe in the under, As to Perpendicu-
lars, they are always perpendicular,

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PRACTICAL
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43 PERSPECTIVE

Of the Line of ELzvarion, Jerving to give the Heights of
all Kinds of Objeéts in all Parts of the Plan. es

T H E Ufe of this Line is of the laft Importance, infomuch, that whoever is
perfectly Mafter thereof will fcarce meet with any Difficulty inany Kind of
Elevation. :

As inthe putting Planes in Perfpective we made ufe of the Bafe Line; fo in
Elevations, another Line is to be ufed, to direct us, and carry the proper Heights
to all the Objects to be raifed: '

This Line of Elevation muft be perpendicular to the Bafe Line AB, which is
always the firft Line of the Plan, andthat next the Eye, and of Confequence the
fitteft to carry the Meafures to the feveral Objects in the Plan. On this Account
the Line of Elevation CD is raifed perpendicularly.on AB, as the other Lines
in the Plan fhould be : Infomuch, that itis to be remembred as a Rule, that when-
ever, in the Courfe of this Work, mention is made of Perpendiculars, it is to be
underftood of Perpendiculars to the Bafe,

Since ’tis this Line of Elevation whichis to receive and give the Heights of the
Objects to be rais’don the Plan, it muft have the fame Horizon with the Plan ;
for this Reafon, from the Foot of this Line (which is placed either on the right
or left) a Line is to be drawn to fome Partof the Horizon, tho’ to what Part does
not matter, the Effect being the fame in all. In this Figure, the Line of Ele-
vationisC D, and from C, the Line isdrawn tothe Point of the Horizon in E.;
Or it might be drawn to the Point of Sight, if one pleafed. We have here put
the Line of Elevation on either Side, and the Point different ineach, to fhew that
it will anfwer any where.

If from the Point H, which is inthe Plan of the fecond Figure, you would
raifea Line of two Foot Height, fet two equal Parts on the- Line of Elevation,
which you hold equivalent each to one Foot, fuch is here CF ; and from C draw-
ing a Lineto E, you will have an Elevation of two Foot between the two Lines.
Cand F,

Now, to give the fame Height of two Foot to a Line raifed from the Point
H, from D draw an occult Line parallel to the Bafe Line, till it meet the Line
CE inthe Point]; then from the Point I ereét a Perpendicular 1K : This will be
the Height of the Line required, which is to be taken hence in the Compaffes,
and fet off from H toL. !

If a Line likewife two Foot high were required to be drawn from the Point
M, the fame Operation being repeated, you will have the Perpendicular N O,

which willbe the Height required from M. Laftly, performing the fame for the
Point P, you will have the Perpendicular QR, for the Height of a Line of
two Foot fromthe Point P. —

The fame Rule will give a Height of 3, 4, 5, 10 or 20 Foot; all required
being to fet fuch Heights-on the Line of Elevation, from thofe Heights to
a Lines to the Point in the Horizon, as E, and to proceed with the reft as
above. I

“PRACTICAL 43

Horifon

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44. PERSPECTIVE
BE EQEDEDEDENEDEOENED
ne SO Soe CPEVGOae

ELEVATION of @ Cube ix Perfpective.

H A VIN G made the Plan according tothe preceding Rules, and having put
‘the Lineof Elevation upon the Bafe.Line, on fome Side of the Plan, as FL,
upon the fame Line fet off the Height of the Cube, viz. FM, and from the Points
F and M draw Lines to the Point of Elevation E; then from the feveral Angles of
the Plan ABCD, draw Parallels to the Bafe Line, till they meet with the Line
F E, and from the Points of Interfection F and H, erect Perpendiculars F M and
HK; then taking thofe Meafures in your Compaffes, fet them perpendicularly
upon the Angles ; thus, taking the Height FM, fet it on the two Perpendiculars.
raifed from A and B, which will give you AGandBG:; then taking the Height
HK, fet iton Perpendiculars raifed from C and D, which will give you CO, DO;.
laftly, joining the right Lines GO, OG, the Cube will be raifed.

For the Elevation of any Figure whatever always draw Lines from the feveral
Angles of its Plan, parallel to the’Bafe Line, till they cut the Line drawn from
the Foot of the Line of Elevation, and proceed in all refpects as directed for the
Cube, and you will find there is nothing, however difficult and unequal, but will
be thus brought into its Perfpective. Examples of which we fhall give in the
Polygons following. |

The fecond Figure is another Cube, raifed after a fomewhat different Manner
from the firft. The Procefs we fhall defcribe in few Words,. being nothing con-
ten)ptible.

Having difpatched the Plan the ordinary Way, fromthe feveral Angles thereof,
BCDE, erect Perpendiculars; and on the firft of them, BC, fet off the given
Height of the Cube, viz. BA, CA; then from the Points A A draw Lines to
the Pointof Sight F, orto the Points of Diftance GH, and the Points I and L,
wherein they interfect the Perpendiculars of the Angles D:and E, will give the
Line of Depth, and the Topof the Cube perfectly raifed.

This latter Method is much lefs univerfal than the former, which has always
been in ufe among the oldeft Authors; yet has it fome Advantages, which we may
have Occafion to touch upon hereafter. °

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Elevation of @ TRIANGLE.
U N DE R onr laft Article we promifed to fhew with how much Eafe ail
Kinds of Figures may be raifed in Perfpective, Now of thefe, Polygons,
or Figures of many Sides, are the moft difficult: We fhall therefore choofe to
exemplify in thefe ; and, to obfervefome Order, will begin with the moft fimple,
the TRIANGLE.

Having formed the Plan, as already directed under Ar T. 21, where we have
fhewn the Method of drawing it with a Ledge or Lift: The Line of Elevation,
as juft now intimated, muft be fet on one Side, and of any Height at Pleafure,
ex. gr. BA, which we'll fuppofe to be 3 Foot: Then from all the Angles of the
Plan drawing paralle] Lines, parallel to the Bafe Line, to the Line BE, and from
the Points of Interfection erecting Perpendiculars between the Lines AE and
BE, fet off all their Heights upon the fevera] Angles, whence the Parallels pro.
ceed: The Height AB, for Inftance, on the Angles Gand O, which will give
GT andOV; the Height HL, on the Angle K, which will give K X; and the
laft Height NP, onthe Angle Q, which gives Q Y. Laftly, connecting the
Points R, Sand Y, and again the Points T, V and X, by Right Lines, you
will have the Triangle in its proper Thicknefs, (7c, |

BEBO 2G IEGSIICIOITIOOG 99 III IYO : CSOT IOUN’ 9ILEINI

A Pentacon, or Five-Angle, iz Per/pettive.

#9 HE Pentacon, we have faid, is a Figure with five Sides or Faces,
and as manyAngles ; and have direéted the Method of forming it in P. 22,
Asto the making its Elevation, we fhouldlofe Time to defcribe it, the Figure
hereto annexed fhewing abundantly that its Method is the fame with that of the
Cube and Triangle,

Pde sd ct duh ca ccd ddd dad hdd ad

The Huxacon, or Six-Angle, in Per/peétive.

o HE Hexacon isa Figure with fix Angles, and as many Sides or Faces,
as already obferved, P. 23 and 27. where we have given its Diminution,

The Method of raifing it is obvious enough from the Figure,

PRACTICAL

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46 PERSPECTIVE

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Begacocsoseceocsuenenseoe soceabances SISOS

The Hertacon, or Seven-Angle,
in Perfpective.

HE Hepracon 1s a Figure with feven
Sides and Angles ; ; the manner of defcrib-
tng it, and of putting its Plan in Perfpective, we
have already given in Page 24. Its Elevation is
performed after the fame manner as that of the

Triangle, as canine from Lg. I

The Octocon, or Fight-Angle, 7
Perfpective.

HE OctocoN ssa Figure with eight Sides

A and Angles, as reprefented in Pag. 25, 26.
where the Reader will find two Ways of putting
it in Perfpe€tive. Its Elevation is the fame as that
of the preceding one.

PRAG TIGA L. £6

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A Double Crofs zz Perfpective.

“* HIS and. the following Figure we add from the Sieur

de Marolois, who has put them in his Works according:

to our Method. The Truth is, it were fomewhat difficult to
put them in Perfpective any other way, by Reafon of the
Multiplicity of Angles; but in this Method all is eafy, by on-
ly raifing the Heights from allthe Angles of the Plan, &c. as.
already obferv’d of Polygons, and is evident from the Figure.

A Stone fluted, or channel?’d flar-wife, in
: Perfpective..

OT having given the Plan of this Figure among the:

_ other Plans, we have judged proper to add it under-

neath. The geometrical Planis eafily made, as being only a

Circle divided into fix, and the Diviftons joined by right Lines,

leaving a Point between each two; as, ex. gv. between 1 and 3,

leaving 2; and from 2 to 4, leaving 3; and fo of the other.
The reft is obvious from. the fecond Figure. : :

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48 PURSPECTEIWE

Of Pinasters in Perfpeétive.

N the raifing of Columns, Pilafters, Walls, or the like Objeéts, which are

to beof the fame Height, there is no need of a Line of Elevation ; ’tis fuf-
ficient to proceed as in the fecond Method for the Cube, that is, having raifed
Perpendiculars from the Angles of the Plan, as here from ABCD of Fig. 1.
fet the Height defired on the firft or fecond Perpendicular, as AF or DE; then
drawing a Line from E to the Point of Sight F, to this Line all the Perpendicu-
lars from the other Angles are to be raifed: In which Cafe, the Pilafters Gand H
will be equa! to the firft.

If one choofe not to make ufe of Squares in the Plan, the Meafures muft be
laid on the Bafe Line, and Rays be drawn thence to the Point of Sight F, and
other Rays for the Diminutions to the Point of Diftance K: Thus, ex. gr. LM
being a Side of a Pilafter, Rays are to be drawn from the two Points thereof,
Land M, to the Point of Sight F, for the Breadths of all the Pilafters ; and for
the Depth of each, as they are intended to be fquare, the Diftance LM is to be:
taken and fetoff from L to N; thendrawing a Lineto K, it will give the Depth
of the Pilafter in O; laftly, from the Points LMO erect Perpendiculars, and
proceed as above directed. If you would have the Width of two: Pilafters between
One and another, fet them accordingly on the Bafe Line, and after making the
Depth of the fecond Pilafter equal to the firft, as here PQ, from the two Points
P Q draw Lines to the Point of Diftance K, which will give the Points RS on.
the Ray L; and from S draw another little Parallel cutting the Ray MF, as the
Line ST ; laftly, from the three Points R, Sand T erecting Perpendiculars; pro-
ceed asin the former Cafe. A third, fourth, &@c. are to be added after the
fame Manner, ftill obferving the fame Meafures on the Bafe Line as in the firft
Figure.

Of Pitasters viewed by the Angle.

W E have already obferved, that the Plan of Squares is formed by drawing

Lines from the Divifions of the Bafe Line to the Point of Diftance. As
to the Elevations, the Method is the fame with that juft defcribed : For having.
fet the Height AB onthe firft Perpendicular, Lines muft be drawn from the
Point B.to the Points of DiftanceC D, which will interfec&t and give the Heights
of the other Perpendiculars raifed on each Side ; then giving the Diftances re-.
quired between the two Pilafters, which are two Squares, raife the fecond ; and
by the fame Rule the third. Their Heights will be found by drawing a vi-
fual Ray from the Point Bto the Point of Sight E, the Interfections whereof with
the firft Perpendiculars in the Points F andF, as alfo the Interfections of other
Lines from F and F to the Points of Diftance C and D with the other Perpen- _
diculars, will give the Heights required, as in the firft Pilafter.

Thofe done without Plans muft have their Meafures on the Bafe Line, as if
they were to have the fame Breadth with thofe viewed in Front. Accordingly,
the Breadth G H muft be marked, and a Ray be drawn from G to the Point
of Sight E, which will give all the middle Points, or Diameters. Then fetting,
the fame Breadth from Gtol, from the three Points GHI draw Lunes to the
Points of Diftance CD, which form the firft Plan. On this Plan erect Perpen-
diculars, on the firft whereof fet off the Height, as GK, and from the Point
K draw Lines to the Points of Diftance, which ‘will give the Shortnings of the
Perpendiculars of each Side. For the fecond Pilafter,; do the fame with the
Points L. and M:: And for the third, with the Points NO. The reit is evident
from the Figure, ae,

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Effect of the Difference of HoRIZons.

pi H E higher a Man israifed above an Obje@, the more he fees of the
upper Part thereof; of Confequence, the lower he is, the lefs he
fees; andif he be underneath i it, he only fees the bottom Part, and nothing
of the Top.

The firft Propofition is evident from Fig. I. the fecond from Fig. IT. and
the third from thelaft.

The firft and fecond Cubes are formed after the manner already AeSideted,
The third is alfo done by the fame Rules, tho’ they may appear fomewhat
more difficult, by Reafon the Obje@ is feen over-head; but, inverting ‘the
Paper, or Painting, and drawing Lines to the Point oF Sight A, and Points
of Diftance B and C, as in the former Methods you —will have the fame
Facility. We fay nothing of Objects viewed fide-wife, as having already
fo often repeated, that the Method isthe fame as of thofe in Front. To
render the Practice of putting them in Perfpeétive more eafy, ‘we have ad-
ded two Figures, the one abare Out-line, the other fhadowed farther.

Before we quit this third Figure, it is to be obferved, that the Low-
nefs of the Horizon is the Reafon we fee the Bottoms of Objects, as DEF,
whereas of thetwo others, GH, placed in the Horizon, neither Top nor
Bottom can be feen: Not the Top, by Reafon of the Lownefs of the Hori-
zon; nor the Bottom, becaufe they are the Horizon itfelf.

There are Abundance of Painters faulty in this Point, making no Scru-
ple to > thew the Tops of Objects, even where the Horizon is very low. 3

49

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TFRACTICAL

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Elevation of ObjeQts view'd by the Angle.

W E have already fhewnin p. 19, 20. how the Plans are to be form’d, the
Lines being always to be drawn to the Point of Diftance, not to the Point
of Sight, unlefs for finding the Diameter: The fame Rule is to be obferved for
the Elevations, as is evident from the firft Figures, all the Lines whereof are
drawn towards the Points of Diftance B and C, and none of them to that of
Sight A. : |

“The firft Figure D fhews that tho’ there be an infinite Number of Parts in any
Object feen Angle-wife, they are all to be drawn to the Points of Diftance B and
C. If youwould do one after the fame manner, the Rule isthis 5 having formed
a Plan, and raifed occult Perpendiculars, as already directed, fet the given
Height on the firft Angle, as EF, and from F draw Lines to the Points BC,
for the Heights of the fecond and third Angles, in the Points G3 then from G
draw Linesto B and C, and you will have the fourth Angle of the Platform.
The other leffer Pieces are raifed’ after the fame manner, viz. by fetting the
Heights on the firft Perpendicular, as from F to H; and from H drawing Lines
to the Points C and B, as before done from the Point F : By fuch Means you
will have the Heights of all the Angles, and the Points I and K will give the
Thicknefies of all the leffer Pieces, and the Platform of the Middle, by ftill
continuing todraw Lines tothe Points BandC. The reft is evident from the
Figure, which may: ferve fora Caftle defended with four fquare Towers, or for a
Palace cantoned with four Pavilions. : : :

The two other Objeéts on each Side the great one are feen Side-wife ; the man-
ner of drawing them is in all refpects like thofe viewed in Front: Thus, raifing
Perpendiculars from all the Angles of the Plan L, and giving the neceflary Height
to the firftof them, as MN, and drawing a Line from the Point N to the
Points of Diftance BC, you will have the fecond and third Angles in the Points -
‘OO ; then drawing Lines from O to the PointsBC, you will have the fourth An-
gle, which isthe Elevation of the whole. This is according to the firftt Method ;
the fecond would have given the fame. oe

The fecond Figure underneath is done the fame Way; all the Difference is,
that in this the Horizon is fomewhat lower.

The third fhews the Bottom of the Objects ; but the Method is ftill the fame
as in thofe that fhew the Tops, the Lines being drawn to the Points of Diftance
‘QR in the horizontal Line. von

We=saea~

S49
Horizort,

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Pee TEC A&E:

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Br PERSPECTIVE

ocoo i PDooepao Coo os Ceow sos og Sees’ OES

To raife Objeéts of any Heights, and remove them to tissy Dif
tance at Pleafure.

C UPPOSE it required to have an Object two Foot high, one Foot broad,
and one Foot deep; and another three Foot high, one Foot broad, two Foot
deep, and two Foot diftant from the firft Object; and another a. Foot broad,.
five Foot deep, four Foot high, and three Foot diftant from the middle Object 5,
your Method of proceeding will be thus: Having formed a Plan of Squares,
fuppofed each equivalent to one Foot, by Means of the Points of Sight A, and
Diftance BC ; from the firft Angle ere&t a Perpendicular according to the fecond
Method above directed, which Perpendicular is to. carry the proper Meafures to:
all the Objects, as here D E, wherein the Meafure DF is fet four Times, by Rea-
fon the higheft Objeét is not to exceed four Foot. From the feveral Angles of
the firft Square FI GD erect occult Perpendiculars 5 and having fet the proper
Meafure, viz. two Foot, on the firft of them, D, from the Point 2 draw a Line
to the Point of Sight A, and it will cut the Perpendicular of the Angle Gin the
Point H, through which a Line is to be drawn parallel to the Bafe, cutting the
Perpendicular ofthe Angle T in K, and another Parallel to be drawn through the
Point 2, cutting the Perpendicular of the Angle F in the Point Ls then con-
necting the four Points HK L and 2, by right Lines, you will have the firft Ob-
jeét. Now as youwould have a Space of two Foot between the firft and fecond
Object, two Squares are to be left vacant between them; and on the firft Angles.
of the third, Perpendiculars are to be raifed, and the fame done as to the firft Ob-
je@, with this Difference, that the Height of the fecond is to be taken from the
third Point of the Line DE, by Reafon it is to-be three Foot diftant, and that it
is to take up two Squares, fince it isto be two Foot deep. Between this fecond
and the third Object the Space of three Squares is to be left, by Reafon there are
+o be three Foot from the one tothe-other. From the firft Angles of the fourth
Square Perpendiculars are to be raifed as for the firft Object, and five Squares
farther, another Perpendicular for the Line of the Depth, and the Bound of the
five Foot, whichis the Depth of this third Object. The fourth Point of the Line
DE gives its Height, four Foot, by cutting the Perpendiculars, as in the frft
Objeét. The Objects on the other Side are raifed in the fame Manner, and
on the fame Proportions as thefe; but the Wall in. the Middle is of an equal.
Height every where, viz. four Foot, with an Aperture of three Foot in the
Middle. ~
Inthe fecond Figure are three Walls of equal Height; whereof that in the
Middle is a Square deeper than the two extreme ones. Detweel) each is an A’per-
ture of three Foot, for Doors or Windows. On the other.Side is a continued
Wall fourteen Foot long, and ofan Height anfwerable to the reft.. “The Method
of elevating all thefe, is the fame with thofe above. What we calla Wall may
likewife ferve for a Hedge, Pallifade, &. of a. Garden.. —

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Of Wauts viewed in Front.
ROM what has already been faid one may raife Walls of all Kinds in any
oblique Views; and tho’ the fame Method may ferve for the fame Walls
viewed in Front, we have thought proper to add this Figure on two Accounts :
it, By Reafon itis not always that Plans are made, and on fuch Occafiona Man
would be alittle to feek for the Thickneffes. 2dly, To give the Thickneffeés to
Gates and Windows, which might occur in fuch Walls.

To make Walls parallel to the Bafe Line, or the Horizon, on a Plan, one may
give them any Length at Pleafure on the Parallels to the Horizon. For their
Breadth, you may take thatof a Square, from the Angles whereof AB, you are
to ereét Perpendiculars to any given Height, as C; from C draw a-Ray to the
Point of Sight D, and CD will give the Diminution of the Wall.

When there isno Plan, the Thicknefs of the Wall, as EF, is to be fet on a
Parallel to the Bafe Line in the firft Corner of the Wall; then from Fa Line is
to be drawn to the Pointof Sight D, and from E, another to the Point of Diftance
G;; and from the Interfection of the two in the Point H, a Perpendicular to be
raifed, and another from the Point F : Then the Height of the Wall FI is to be
taken, and from1a Line to be drawn to the Point of Sight D, the Interfeétion
whereof with the Perpendicular H, will give the Diminution of the Wall. For
the: Length, you may give it at Pleafure on the firft Parallel EF. For
the Doors and Windows in the fame Walls, mark the Width and Height as here
K LMN, and fet the Thicknefs required on a Parallel, either above or below the
Doors or Windows, in the Corner next the Point of Diftance, as here NO or
LO; laftly, from the Points L and N draw Lines to the Point of Sight D, and
from the Points O to the Point of Diftance G, and from the Interfections of thofe
Lines in P, 8c. draw the Thicknefles.

- Another W arr viewed by the Angle. .

H AVING the Plan, you have nothing to do but erect Perpendiculars from

AL the Angles already determined, and to mark the Heights on the Perpen-
dicular from the Angle next you, as on the Line QR; and from the Point R,
to draw Lines to the Points of Diftance ST; the Interfections thofe Lines make,
with the Perpendiculars raifed from the Angles of the Plan, will give the Length
and Thicknefs of the Wall. If you have no Plan, fet the Meafures both of the
Breadth and Depth of Doors and Windows on the Bafe Line, as in this Example,
V Xis the Breadth, XY the Depth, and Z x the Height of a Window ; then
from all thefe Points draw Lines to the Points of Diftance ST; firft from X,
which is the Ray of the Bafe; thenfrom V, a little occule Line cutting the Ray
X Sin the Point 5, which is the Thicknefs of the Wall. As to the Depth, the
Ray YS will give it by its interfecting with X T in the Point 6; and Z 1 will
give the Breadth of the Window in the Points 7, 83 from which Points im. 6, 6,
+, 8, Perpendiculars being raifed, and the Height 2 being fet on the firft of
them X, and from the Point 2 drawing Lines to the PointsS T, the Interfections
with the Perpendiculars will give the Height of them all. From the Height of
the Window, marked 3, 4, draw Lines to T’, and where thefe interfect the Per-
pendiculars 7, 8, Lines are to be drawn ; and from the Corners g to S, for the
Depth 10, draw Lines to T; and from the Point of Interfection 11, draw a Per-
pendicular. This now may ferve far a Pallifade as well as a Wall.

PRACTICAL

A MORES LETRAS A

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To place a Door in any Part of a Wall at Pleafure.

: Wall is to be raifed one, two, or three Foot thick, on the Points HI, and

to be carried on of the fame Height, as already directed. If then you
know pretty nearly the Dimenfions of the Door, fet the Breadth on the Bafe
Line, as here in ABof the lower Plan, containing three Foot, and a Side of A
and B fet the Breadth of a Frame, or Band, Dand C, and from ABC andD draw
Lines to the Point of Sight K ; and where they cut the Parallel MN in the Points
OO, Gc. erect Perpendiculars of any Heights at’ Pleafure : Thus is the Width
of the Door already got. For its Height, DF E is to be transferred from the Plan
underneath to the Corner of the Walll, and Lines to be drawn from the Points
FE toK ; and where they interfect the Perpendicular M P in the Point Q, draw
QR parallelto MN, which will give the Height of the Door, andthe Band or
Framea-top. Its Thicknefs, or Depth, will be the fame with that of the Wall,
whichisGF. And if from G you draw a Line from the Point of Sight K,: ic
will cut the Perpendicular M P in the Poirtt S, through which drawing ST paral-
Jel to QR, you will have the Thicknefs of the Door V.

To make a Door ina Side-wall, the Inftruétions given in Pag. 17. are to be
well remembered ; importing, that all the Meafures are to be put on the Bafe
Line ; and, that Lines being drawn from thefe Meafures to the Pomtof Diftance,
will give all the Diminutions defired. Foran Example, a Door four Foot broad
is defired ina Chamber. Set off four equal Diftances: from I to C, and draw
Lines from the Dimenfions of the Door C A and BD to the Point of Diftance L 5
where the Ray I M interfeéts thofe Lines, erect Perpendiculars X Y, which will
give the Breadth of the Door. For its Height, draw Lines from the Points E and
F to the Point of Sight K, and the Interfections with the Perpendiculars will give
the Height. Asto the Thicknefs of the Top and Bottom, drawthe Thicknefs
of the Wall, GHand FI, to the Point of Sight K then drawing a little Paral-
Jel to the terreftrial Line, ‘through the lower Corner of the Door X, and another
through the upper Corner, you will have X Z, the Thicknefs of the Top and
Bottom, to be joined by a Perpendicular, as you fee in the Figur:.

If you would have a Door on the other Side, you have nothing :o do but draw
Parallels to the Bafe Line from the Point X to the Ray IN, and then raife them
as already directed. The reft is the fameas on the other Side. The Gate is not
here reprefented in the Middle ; which isa Thing we did defignedy, to obviate
the Error of fuch as, without any other Meafures, draw two Diaonals through
their Painting, tho’ of ever fo great a Size, and make all their Objects equally
diftant from the Interfection of thofe Lines, 7. e. from the Middk of the Paint-
ing : So that, on their Principle, a Body fhould always be mountd to fhew their
Work in all its Advantage ; which isa palpable Overfight. For ho’ a Painting
fhould be forty Foot high, andit fhould be placed on the Ground 0 be feen, the

Horizon fhould never be above five Foot high, but rather lefs thanmore ; where-
as in their Way the Horizon fhould be twenty Foot high. io A

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PRACTICAL

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64. PERSPECTIVE

To draw Winpvows in Perfpeétive.

Pee Method of defcribing a Window is perfe€tly the fame with that of a
Door ; for if there be any upright Poft, of Wicket, in a Door, .’tis no
longer a Door, but a Window: So that you have nothing to do but learn to make
a fingle and double Crofs, and you are Mafter of Windows. Suppofe now ’twere
required to make one ina Wall AB, of any Breadth at Pleafure, lay down its
Breadth on the Bafe Line, as. DE, anc fromthe Points D and E draw Lines to the
Point of Diftance F, and ftom the Interfections GG, of thofe Lines with A C,
ereé&t Perpendiculars GH, GH giving the Width of the Window, which is here
only two Squares, or Panes. Astothe Height, it is ufually raifed as near the
Cieling as may be, but the Breaft-part fhould not be above. three Foot and half;
this Meafure therefore is to be fet on the Perpendicular AB, as from A to I, and
drawing a Linefrom Ito K, where thac Line interfects G H, will be the Breatt-
part. After the like manner drawinga Line from L, the Top of the Window,
to the Point of Sight K, its Interfection with GH, will be the Top of the Win-
dow ; by which Means we fhall have a long Square, or Parallelogram, to which
a Crofs being added, will form a Window. To make this. Crofs, the Space DE
> shuft be divided into two equal Parts, each being about half a Foot; then draw-
ing this Breadth M tothe Point of Diftance F, and from the Interfeétions thereof
with the Ray AC, erect Perpendiculars N O for the upright Poft, or Stancher,
inthe Middle of the Window. Ass to the Crofs-pieces, you may add as many as
you pleafe, only obferving that their Thicknefs muft be equal to that of the up-
right Piece ; taking the Meafure M therefore fet it off upon the Perpendicular
AB, as is P, and drawing a Line from P to K, the Points wherein it interfeéts
the Perpendiculars GH, GH will give the crofs Bars, and of Confequence the
Window is finifhed. For its Thicknefs, ’tis here only to be half thatof the Walls
to accommodate which, occule Lines muft be drawn from the Point QtoK, and
little Parallels to the Bafe being drawn from the Corners of the Window S, the
Point wherein they cut the Line Q K will give the Thicknefs required.

This Window ranges even with the Wall on the Infide, which is not very ufual,
‘Windows being now frequently made with Embrafures, or Niches entering into
the Wall a Foot, or lefs.

The Method is precifely the fare in both, only that inftead of taking the In-
terfections on the Line AC K, they muft here be taken in another, re-entering
into the Wall as much as the Window is nade to re-enter, as appears, from the
lower Figure, where the Ray OK receives the Meafures laid on the Bafe Line;
and thatall the reft muft be drawn to the Point of Diftance F, as in the former
Cafe, taking the Thicknefs of the Window between the Perpendicular OQ, and
the other F, which is the laft. Laftly, when the Window is finifhed, on the
Ray OK, and from the. Breadth of the Wall OF, raife the Perpendicular A,
and draw it to the Point K3 then from the lower Corner of the Window, in
the Points P P, draw a little Parallel cutting AK in Q, which will be the Thick-
nefsof the Wall, covering the Window a little, and fhewing the Thicknefs R P;
then from the Point R erecting the Perpendiculars RV, cutting the Ray TK
in V: which will be the Thicknefs of the Topof the Window. From the Mea-
fures here laid done, one may make as many as one pleafes, ftill obferving the
fame Order, 9 3

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PERSPECTIVE

EDEN EGOENE
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Of CIELINGS.

Bag ok we ought in fome Meafure to follow thé fame Order that the
Masons obferve in raifing a Building from the Ground: The Pavement, or
Ground-work, is their Foundation, whereon they raife Walls, which they pierce
in as many Placesas they pleafe for Doors and Windows.

Suppofe the Walls raifed AB, on which Beams are to be firft laid, and over
thofe, Joifts or Quarters 5 having meafured the Square of any Piece (which we
here fuppofe a Foot) it is to be carried to the Top of the Wall, as CD, and
from the Points Cand D occult Lines to be drawn to the Point of Sight E,
which will give the Rays CDGF. The fame Meafure C Dis likewife to be fet
on a Parallel to the Horizon DH, whereon all the Meafures of the Joifts, &c.
to be laid on the Wall, are to be difpofed, as we have here done the three I, K
and L.; then drawing Lines from all thefe Meafures to the Point of Diftance M,
and from the Interfections with the Line DF, in the Points O, O, &e. letting

cutting the Rays CG ‘athe Points P, P, €. and laftly,
e Horizon through the Points O and P, you will have

orderly laid: As in the firft Figure. !
upon the Beams, or, more properly, to mortaife them.
o ferve as a Bafe Line whereon to lay the Joifts in fuch
i{tance from each other, as fhall be judged expedient 5
apart from each other. To
he Beam QS, fuch as QT, ©
and draw an o and FV, range the Joints,
X, X, €. and from all their Angles that are vifible, draw Lines to
the Pointof Sight Y. Andthat they may not exceed the half of the other Beams,
from the Middle of the firft, which is the Point T, draw an occult Line to the
Point of Sight ¥, which will cut all: the other Beams in half, in the Point Z 3.
laftly, from the Point Z draw Parallels to the Horizon, that you ,may not pafs
them in drawing Lines from the Joifts to the Point of Sight. If you don’t care to
take fo much Pains, fet the Joifts Z, on the Line QR, asthey are underneath 5.
then draw Lines boldly from one Beam to another, fromall the Angles of X, xX,

&¢, tothe Point Y, and you will'have what you require.

PRAGViGxn Me

sa
——

co ill

: Be es

4
FE =

oe AN

MN

=.

Hl

PERSPECTIVE

36
50 SAE ALI I OES OPPO OS
32, Of 2G, FRG se Ta, eG ONO

De 0D Gt
ap ae (de dae. desde eae

ne ds

L HIS Froure is only wlaed to fhew the
Effet of the Method juft now laid down 5
wherein it is obfervable the Number of Stories
does not render the Practice at all the more

difficult.
The Joifts are not mortais’d into the Beams of |

the upper Story, as they are in ee lower.

56

gnu oi ae a

ars

|

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es

Ba

==
==
|

a

PRACTICAL

a meme
i=
i
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Tans re i

a ae ere oy semen 6

$y PERSPECTIVE

C8

a Gee Gen Gees Ge Gaus B® Gene ays

Another Difpofition of CEI Lincs 771 Perfpeftive.

- FITS Method is performed in all Refpeéts like that juft defcribed, only that

& the Difpofition of the Members and Pieces that compofe the Cieling i to
be changed ; thatis, the Beamsare laid long-ways, tending towards the Point of
Sight, and the Joifts a-crofs, which is the reverfe of the former. ,

Suppofe the Walls AB; on thefe, or on Confoles jutting out from them, fet
the Thicknefs of the Beam CD, and through the Points C and D draw Parallels
to the HorizonCE and DF, between which you may putany Number of Beams
at Pleafure, as we have here done three, viz. GH and I, from all which Lines
are to be drawn to the Point of Sight K ; then through the Point P, wherein
D P interfects the Perpendicular LP, draw a little Parallel to the Horizon PM,
this will be the Bound of all the other Rays, asG N, €%c. laftly, from the Point
N erecta Perpendicular NO: And fo of the reft. Thus much for the Beams.

To lay the Joifts a-crofs the Beams, fet their Thicknefs on the Line QR, as”
V.V-V; and from the Extremes of V draw Lines to the Point of Diftance S 3
and through the Points of Interfe&tion with the Ray QT draw Parallels to the
Fforizon, as far as the Beam of the other Side, If you would mortaife them in
the Beams, take the Thicknefs of the Rafters within the Beam, as Q xX; andfrom
X draw a Parallel to the Bafe Line, as far as the other Side X X ; and between
the two Lines QRand X X fet the Divifions VV, &%c. which will form YY,
ésc. And fromall the Points ¥ drawing Lines to the Point of Diftance S, you
will have the Thickneffes of the Bottom and Sides given by the Interfeétions with
the Ray X T in the Points ZZ, &<, through which drawing Parallels to the
Horizon, the Ceilings will be finifhed ; as in Fig. II.

Thus it is that fimple Timber Ceilings are put in Perfpective. If, after thefe,
or in Lieu of thefe, you would have a handfom Platform of Painting, or other
Enrichment, you will find Inftruétions for the fame in Page 35. where we fpeak
of Gardens: And making Ufe of the Line QR fora Bafe Line, you may do
what you pleafe therein. |

For Floors, there are enough already laid down in Pag. 30, 31, 32, 33, and 34.
to open, the Mind for the finding many others. Thus far we have had to do
with the Rooms, as Hall, Chamber, or the like, the feveral Parts whereof are
fully.delivered ; The Moveables therein fhall be fhewn hereafter.

: | ;

sili ec i

iT i TT

~~

La

_—— it Liunnrnelt _ =

a WR :35= tren eSATA SERRE ee AEA: RT RARE NRT SOON RN me ut MN |

58 PERSPECTIVE

sucsescouceseceseoeninatesocecent ee
D Og ee S
OO ee ae

SOCOM GOVT Gea s guesee ees eGoencoaGaes. G8bG

HIS Figure fhews the Ciehing juft now de-

{cribed, diftinét and clear of the Lines
wherewith the former was embarraffed.

The Conftruction of the Gate fhall be fhewn
hereafter. 4

‘ere PASO Shae = A LAR a
= a po uSEB ere Rne ae ve eee

ae
<<.
O
a
bea
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f.,

-

/

89 PERSPECTIVE

CORE ODO EAE OLEH REIS NEM

ae SE es % . ats Hea
PUN CEN ENTE ES

CSO RRBASS IKEA RRE ITI

FF) OCS EER GAR O—O
See Skee Tite Be Si S18 SEI
RBH) BEDS (KR KPEYKBHRSHO

Circular GAT ES and ARCHES wewed directly.

H AVING given fufficient Inftru€tions for Halls, Chambers, Win-
dows, and /quare Doors, or Gates, we proceed to the Practice of
round ones. : :

Suppofe then ABCDEF to be Pilafters on a Plan, to place Arches
thereon ; divide the upper Breadth GH into equal Parts, in the Point I,
on which fetting one Leg of your Compafles, with the other, defcribe a
Semi-circle G H, for the firft Arch.

To make all the reft of the fame Height and Breadth, draw Lines from
the Point of Sight HG to the Point of Sight K, and through the two
Points L, L, where thofe Rays cut the Perpendiculars C D, draw Paral-
lels to GH: Thefe Parallels being divided into two, and Semi-circles
truck from them, as in the firft, you will have the fecond and third Arch.
To find the Middle of thofe Parallels L, you have only to lay the Ruler
inthe firft Centre I, anddraw a Lineto K, which will cut them all pre-
cifely inthe Middle MM, and give the Points for the Semi-circles to be
drawn from. ‘Thofe viewed in Front, and thofe by the Side, are all per-
formed-the fame Way ; as appears from the firft Figure.

_ If it be required to make an Edge, or Band, of equal Thicknefs
throughout, you are only to ufe one Center as O, from which the Thick-
nefles N P of the lower Figures are formed. ‘The reft is all performed as
already directed, by drawing Lines to the Point of Sight K. The laft
Figures thew how all Kinds of fimple Vaults, only confifting of a Semi-
circle, are to be formed: As to the Enrichment thereof, we fhall have
Occafion to {peak hereafter. 3 ae

ae
<f
O
sont
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a2
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ra

ALN aN Se le ae

Semmens insomtinaneeen ee

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!

mT

SB

PAA

a

Sex Bax COO x, COs. He

Yr ~ ExCe
POS ee

Round Arcues over Pilafters viewed in Front.

oT E Out-line of the laft Plate readily direéts how this is to be done,

the Method being the fame in both. In the prefent there are a few
more Lines, but notany Thing more of Difficulty: For, drawing Parallels
to the Bafe Line over the Tops of the feveral Pilafters AB, CD, and di-
viding the firft of them into equal Parts, from the Middle E, as a Center,
defcribe the firft Semi-circle AC, without removing the Compaffes, from
the fame Center, defcribe the Band or Thicknefs AGF C; laftly, fromthe
Center E, drawing Lines to the Point of Sight H, theRay EH will give
the middle Roints of all the Parallels for defcribing Semi-circles over them
all, from BD to the laft, I. The Method is the fame for that in the

Side- view.
CAAA AGAR ASR SAGARA AACA AGA C AC AGRA CACACASASACLCAGAGAS

Gotruic Arcu, or Arch im the third Point.

y jie drawing of this is aseafy as that of the circular Arch. Ha-

ving laid down the Breadth K L, fet one Foot of your Compaffes in
K, anddireéting the other to O, ftrike the Arch LO; then remove your
Compafies to ly defcribe the Arch KO, and you will have an Arch zz the
third Point, KOL. Do the fame from M and N, and you will have the
fecond, or inner Arch,M PN. The fecond Figure, zu the third Point,
has a Band or Lift all round it, which is defcribed from the fame Centers :
Thus, ex. gr. from the Center Rthe Arches SX and TV are fwept; and
fromthe Point S the Arches Q V and R X: All the reft is drawn to the Point
of Sight Y.

Keowee third Point, or terzo Acuto, is reprefented in Figure +-; the
Diameter whereof, a 8, being divided into three equal Parts X, and one
Foot of the Compaffes fet in one of the Divifions, asc, and with the other
the Aperturec é taken, the Arch Je is {truck therewith; then remoying the
Compaffes to d, the Arch dae is ftruck, whichis an Arch in the ¢hird Point
as well as the former ; and either of them may be ufed at Difcretion, Thofe
in old Gothic Churches come neareft the former Kind, ,

re)
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e add ih Arbour of a Garden, the
Performance whereof is in'‘all Refpects the

PERSPECTIVE

Sequel of the former V1 GURE
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PRACTICAL

SiP Ease VY E

ad

SEAS OS OS On Oks OR IONE
Sido Sido lke Eide ike ERs Skee Sido Hive

To deferibe, and put-in Perfpelfive, round Arches azd Doors.

n° H E Circle being fomewhat difficult to put in Perfpective, requires a Num-
ber of previous Lines and Points : To find which the more readily, the firft
Figure here added isto be underftood ; which fhews, that to defcribe a Semi-
circle upon a Diameter AB, there needs no more than to fet one Foot. of your
Compafics in the Point C, in the Middle of AB, and with the other to fweep a
crooked Line from A to B. And thus is the Semi-circle to be transferred upon the
ElevationDE, Fig. II. for a circular Gate or Arch. |

Now to put it in Perfpeétive, it is to be divided intoany Number of Parts,
andthe more thebetter ; as already obferved in Pag. 28. and as we fhall hereafter
have occafion to fhew, when we are {peaking of crofs Vaults. The prefent Semi-
circle we fhall only divide into four, and that by drawing a Parallel to AB, raif-
ing itinthe Point F, which Point will be the. Middle of the Semi-circle; then
erecting two Perpendiculars from AB, cutting the Parallel Fin the Points GH,
and from the Corners ABGH drawing two Diagonals A H, GB, interfecting
each other in]; from the Point I raife a Perpendicular CIF cutting the Circle in
two: And the Diagonals will cut it into two other Parts in the Points KK, thro’
whicha Line LK is to be drawn Parallel to the Bafe Line: All which Divifions
and Meafures are to be transfer’d to Fig. III. to put it in Perfpective.

Firft then draw a Line from the Angle E to the Point of Sight M, and ano-
ther from the Point N (which is the fame Diftance from E, as D is) to the Point
of Diftance P ; which latter cutting the Ray EM in the Point Q, EQ will be the
Width of the firft Arch DE in Perfpetive. Then drawing a Line from O to
the Point P, it will cut the fecond Arch in the Ray EM, or the Point R. As
there isno more Room on the Bafe Line to take the third Arch, a Point muft be
drawn from N to the Point of Sight M; and through the Point R a Parallel to
the Bafe Line RS: Now as RSis under the fame Angle with EN, it is the fame
Breadth, as has been already proved in the Beginning of the Book; therefore
drawing a Line from S to P, it will cut the Ray EM in the Point T, which gives
the third Arch.

Proceed then to raife Perpendiculars V V, &c. from the three Points QRT,
which interfeCting the Ray HM, will give the higheft of the Arches; then from
the Ray BM, which gives the Bottom of theSemi-circle, draw Diagonals BV,
HX, which interfeéting each other, give the Place of the Perpendicular Y F,
that divides the Arch into two; and drawing the Ray LM, it will cut the Dia-
gonals in two, andthe Arch in four ; laftly, connecting the Points BZ, FZ X,
with curve Lines, you will have the firft Arch: Anda Method which will give
you infinite others. The fame ferves not only for Arches and Doors, but alfo for
Vaults, Bridges, and other Things that require the Semi-circle for which Reafon
it is that we decline fpeaking any Thing farther of the two latter.

The fame Method may likewife ferve for Church Windows, only one or two
upright Pofts are to be added to faften the Glafsto, +m

62

PRACTIGAL

be

CR REN ERENT AY Baan aan ee gc
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noe mee at Sa PO one
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63 PERSPECTIVE
frp FOL ALLS NTS A ISIE TN ISS INS TS

To defcribe, and put in Perfpettive, double Arcues and Gates,
i.e. fuch as foew their Thicknefles.

HAT we have hitherto done is merely for the Out-line, which

being doubled gives the Breadths and T hickneffes of Arches,
and what fupports them, by only connecting all the InterfeCtions of each
by Right-Lines: For Example,

Having defcrib’d the firft Line D E, and drawn Lines from D and E
to the Point of Sight A, fet the Thicknefs on the Bafe-Line E C, by
drawing C to the Point of Diftance B, and in the way cutting the Ray
E A in the Point F; thro’ which drawing the Line G F parallel to the
Bafe-Line, it will cut the Rays DA and E A in the Points F G, and give
the Thicknefs requir’d. Then from F G erect Perpendiculars, and from H
draw a Lineto A, the Interfection whereof with the Perpendicular FI gives
the Height thereof. From this Line you are to find the Line of the Cen-
ter of the Semi-circle, by drawing a Line from K tothe Point A, which

ives the Point L, a Parallel drawn thro’ which will have the Center
of the hinder Semi-circle upon it, as N is the Center of that before.
’ ‘This Line M Lis to be divided into two equal Parts, by drawing a Line
from N to A thro’ AO Then fetting one Leg of your Compafles in O,
with the other deferibe a Semi-circle ML, to be divided like that in the
preceding Figure. Laftly, draw Right-Lines from the Divifions of the
one to the other, that is, from the fore Semi-circle to the hind-one, to
conneét. the two into one ; as in the Figure M is join’d to PQ, toR 5,
TY, to AL took, : i

For circular Arches, 9c. view’d in Front, as D EF G, there is no
need of fo many Divifions, ic being fufficient to find the Line M L, in
order for the defcribing of the Semi-circle, which refers to the firft N
PQ; but Ihave made them defignedly, for fear of confounding the Let-
ters with the Lines of the lower Figure, where the Arches are view’d ob-
liquely, tending all towards the Point of Sight Y. Such Arches would
give their Thicknefs by repeating the Operation already laid down for
Fig. I. twice over, and joining the Divifions of the one to the other, as
already obferv’d, and as is exprefs'd in the prefent Figure, to which having
given the Thicknefs E Z, I have drawn the Line E in Dots, and Z a
full Line, in order to avoid Confufion, and to intimate, that whatever
is done with Dots, is not intended to be feen when the Draught is
finifh’d. aa eee

in?
a
t

a Wii 2 . r n \
aii AA

=
<
Oo
na
O
<
m4
Gs

SLES eT SSS S SSS eS es

Another Mutuond for Circular Arches,

'T ETE Arches in Front, which we have hitherto defcrib’d, are all perform’d
to the laft Exaétnefs; but the Procefs is a little long and tedious : we fhall
now add another, equally juft, but much more expeditious.

Having deferibed a Semi-circle, or a whole Circle, BHI, from the Centre A,
from the fame Centre, and the Extreme of the Diameter B, draw Lines.to the
Point of Sight C ; then fetting the Breadth, or Thicknefs requir’d, on the Line
BI, as here D A, from the Point Ddrawa Line to the Point of Diftance E, and
through F, the Point where D E and A C interfect, draw a Line parallel to the
Bafe, till ic cut the Ray BC in the Point G ; this done, fetting one Leg of your
Compaffes in F, and in the other taking the Diftance G, defcribe a Semi-circle,
or Circle, which will be the Thicknefs of the Arch, or Sweep: As is feen in the
Figures. All the Lines KK, &c. are to be drawn to the Center A, and the
others, LL, tothe Point of Sight C. The fame may ferve for circular Windows
built of Stone, in which Cafe the Lines will reprefent the Joints ;: as alfo for
Tons, Vats, &c.

ARCHES viewd Obliquely in Per/pettive.

es HE following Method may ferve when a Perfon is ftraightned, and does
not defire to be fo very exact ; as alfo to avoid a Multiplicity of Lines,
which in the preceding Method is indifpenfible..

Having form’d the firft Arch N Qas already directed, a-crofs it draw little
Parallels to the Bafe in any Number at Pleafure, as here QQ, &c. then taking
in your Compaftes the Breadth of the Spring of the Arch, as PO, fet it off on
the little Parallels Q, by which Means you will have the Points RR; thro” which
a Curve Line being drawn, will form the Thicknefs of the Arch.

°Tis certain, that, according to the Rules of Perfpective, Objects appear the
larger as they are the nearer to us; of Confequence, therefore, the Line OP
fhould be the fmalleft: But the Difference is here fo very fmall, that it is not
worth the minding. Befide, we do not give this as a conftant Rule, but only for
a Shift in Cafes of Neceffity. 2

Y

H

ya

tal
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ERSPECTINE

dar

26, 620, 923.5 2692, FG, OG, 02
& 4

2630,
ay Zell AN é oh a tis oo ad
HC UC UCUG SUSE NL OL

Friar AR CHES.
ae Method of putting thefe in Perfpective is the fame.

with that of the Semi-circular Arches, as appears from
the Figure AB, All the Difficulty isin finding the Out-line,
which is done two Ways. )

The firft by two Centers and a String, the Method already
mention’d for defcribing an Oval; thefe flat Arches being,
in Effe@, Semi-ovals. :

The fecond isthus: Suppofe the Line CD given you to raife
a flat Arch upon of the Height E F, from the Center F defcribe
a Semi-circle © GD, and divide it into any Number of equal
Parts at Pleafure, as is here done into twelve; and from all
thefe Divifions draw Lines to the Center F ; then again, from
all thefe Divifions draw Perpendiculars to the Diameter CD,
as are here the Lines OL; this done, defcribe a Semi-circle
of the given Height of the Arch, as here HEK; and thro’
the Interfetions this leffer Circle makes with the Divifions of
the greater, draw little Parallels to meet the Perpendiculars
falling from the fame Divifions, for Inftance LO, L O, &c. and
- of the feveral Points O conneéted together form the Arch, as
is here done. |

The other Figure makes the Arch ftill flatter, and by the
fame Rules it may be made of any Lowneds at’ Pleafure.

The Figure underneath fhews one of thefe Arches in Per-
fpediive, fuch as it fhould appear, when finifh’d, in a front
View. We fay nothing of the Method, as having already in-
timated it to be the fame with that for the Semi-circle.

S SUEY Se

' ‘

‘
f)
'
4 q
'
*

—————
—<—<———

PRACTIC Ad.

ote tT at SEE SERS PR a oe cr

66 PERSPECTEVE

eS TOO! SO OO ae
CONVO SOLO) “ss OS,
BAGG HUO OHSS COSTCO BOOTIES SSSSH ageeeesoee
I N this Figure we have an Inftance. of ita fine

Fffe& of ARCHES when well center’d, that
is, when they have their juft Rotundity.

For the Steps and Figures, we {hall have ae

fion to treat of them hereafter.

Ln ee

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Le A

PRACTICAL ©

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67 PERSPECTIVE.

COE
B

CRYEED EN) EY OY ES
CICLEVELSIGS GVEDEIESD

To raife ARCHES upon Pilafters on Columns,

CREREDED ENEREDERER ED
5) We)

%

T looks as if there were no Pilafters formed in the laft Figure, for
which Reafon I determined to add this, which may fhew, that the
Method is precifely the fame, and that all required farther, is to leave
Room for the Breadth, &c. of the Pilafter between every two Arches,
which is done by Means of the Plan, or Bafe Line ; as already directed
for Circular Arches. : as 7

. GoTHICcK ARCHES.
(5 otHicK ARCHEs and VauLts, called alfo Arches in the third

J Point, are performed in the fame. Manner as Semi-circles; fo that
having done one, you will do the other with Eafe: The Figure fhews the
reft. As tothe Out-line, we have already fhewn that nothing is more
eafy. The Breadth AB being given to form an Arch of, open your Com-
paffes to the Breadth, and fetting one Leg tn A, with the other defcribe
the Arch BC; then removing them to B, defcribe another Arch AC;
and the Point wherein the two interfeét, willbe the Point or Apex. of the _
Arch CG. ws

As the reft is all performed after the fame Manner as the Semi-circle,
we fhall not repeat it: All the Bufinefs is, that here are Pilafters between
each two, that are not inthe other. This may ferve to confirm and.ex-
emplify what we have already faid, that all that is to be done is to draw
Lines from thefe Divifions on the .Bafe to the Point of Diftance O, which
will cut the Ray DE in the Points FF, &c. for Perpendiculars to be raifed
upon; then fetting off the Thicknefs G, and drawing the Ray GE for the
Breadth of the Pilafters H, from the fame Point H ere& Perpendiculars,
to be conneéted to the other by right Lines, &c, as in the Semi-circle.

4

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68 PERSPECTIVE

CQO ODOC WEEE OO AER CER OO

SHO SSAERRR CaRY De we q W as 26 NTs See TS . aS SS vs RO ob
Hod ee Slee S ESS Kode Slee HOE leo Slee Slee He 3 Se Ro & a ROA,
CCSOLRH ACS SHEE AIO MRI ERY KRY) OCSO MEH KR MRHOCSS

Zo find Cross VaAuLTs in Perfpective.

HE Reader muft remember, or have recourfe to, what we have faid in

Pag. 28. where, fpeaking of putting a Circle into Perfpective, we divided
it, for the greater Exactnefs, into fixteen Parts; but.as in fuch a Divifion there
neceflarily occur a great Number of Lines, we have here chofe to take up with
a Divifionof eight Parts, which if it be the lefs exaét, it will be the lefs confufed.
The other Divifion we fhall refume in the following Page.

Having then formed a Plan of a Circle divided into Gent Parts. 1, 2. 9545/6,
6, 7, 8, Parallels to the Bafe Line are to be drawn through the feveral Divifions
thereof, as far as the Ray BA, which will give the Points CC, Gc. on which
erecting Perpendiculars CD, CD, &. the firft of them, BD, being the Line of
Elevation, all the Meafures of the Semi-circle BE F muit be fet thereon, by
which Means you will have the Points DHG ; from which Rays are to be drawn
to the Point A, and in the Interfections of the Perpendiculars CD, you will
have the fame Divifions as in the firft, fecond, third, fourth, and fifth PLaws.
For a Semi-circle, draw curve Lines as in the Arch of the firft Side, the Divi-
fions whereof areto be transferred to the other, in order to have two collateral:
Arches; from the Springs whereof two Circles are to be defcribed 5. the one before
GH, from the Center M; the other inthe Bottom 51, from the Center N.
And thus you have the four Arches ordinarily found in Crofs-vaults. All that
remains is, to makethe Crofs, or crooked Diagonals, refting on the Corners.
G 5, KL, and paffing through the K or Groin O.

Now as the Circle is divided into eight Parts, the Arches, which are but
Halves of Circles, are only to contain four Parts ; the Semi-circle GK, there-
fore, is to be divided into four Parts, in the Points GP QRQ, which are to be
drawn tothe Point of Sight A, as.far as the Bottom of the Circle5 LL. Now
what follows is the great Secret of the Crofs, viz..That Parallels to the Horizon
are to be drawn from all the Interfeétions of the Circle on the Side 1, 2, 3, 4, 55. /
in fuch Sort, as thatG, which isthe firft Divifion of the Circle, touch the Inter-
fe@tion 1 ina Point; thatfrom 2a Parallel be drawn to the fecond Divifion P,,.
and the Point S to be marked ; that from 3 another Parallel be drawn to the
third Divifion which will give O, the Place of the Key or Groin; and from. 4,
another to the Point T'; laftly, connecting GSOTL with curve Lines, you
will havea Diagonal ; and doing as much for the other Side, you will have the
entire Crofs, and the Vault compleat.

A

68

PRACTICAL:

LC AT NRE ee en tem ye eI Saw a
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69 PERSPECTIVE

FS RI ET
Fserk Regn gga es Gaps asee™ GRO A
Oe es SSS COSTS CNEL:

To draw the fame V wT more ac-
curate.

A MAN, who has a good Notion of the for-
mer Method, will find no great Difficulty in
the managing this; all that is required being to
double the Lines, and take Care of the Interfe-
étions, which are here more numerous, by Rea-
fon the Circle is divided into more Parts.

How to form the PLAN is taught in Pag. 28.
Add, that Parallels are to be drawn thro’ all the
Divifions of the Plan from I to 16, as far as the
Ray AB; by fuch Means you will have the Points
O, O, &¥c. from which Perpendiculars are to be
raifed. ‘The reft, as in the Method preceding ;
over which this has the Advantage of being more
exact, and of drawing the VauLT more eafily,
by Reafon the Divifions are clofer to each other.

69

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PRACTICAL

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40 PERSPECTIVE

| To form narrow VAULTS.

T HERE are two Procefies in this Figure; the one for contracting or ftraight-
f ning Side-vaults; the other for giving the Thicknefs to the Crofs. We
fhall begin with the firft. 7 :

The two Methods for Vaults already laid down, fuppofe them perfectly fquare,
that is, that their Breadth and Depth, or Diftance, is equal ; which holds both
in thofe reprefented in Front, and thofe in Side-views: But @ Perfon only in-
ftru€ted in thefe, would find himfelf ftrangely at a Lofs were he put to conftrud&
a Church, where the Side-arches are ufually much narrower than thofe in the
Front or Middle. :

- We proceed, therefore, to offer you an expedient whereby you'll be enabled
to make the Side Arches of what Dimenfions you pleafe, and that by Means of
the Bafe Line AQ. Suppofe then the front Arch AQ forty Foot broad, and
the Side Arches limited to fifteen or twenty, you are now, according to the In-
ftructions in p. 17. to fet this Meafure on the Bafe Line, and to draw a Line
from the fame to the Point of Diftance, by which you will have the Depth of
the fame Figure in AE. Thus, in the prefent Example, AC being fuppofed
twenty Foot, a Line drawn from C tothe Point of Diftance, (which here is
fuppofed beyond the Limits of the Paper) cuts the Depth twenty Foot in the
Point E; then returning to the Bafe Line, an Arch is to be ftruck at the Di-
ftance AC, and the Line, or Radius, to be divided intoas many Parts as the
larger Arch FG has Divifions, viz. eight; and from the feveral Divifions H,
Perpendiculars HI to be raifed ; and fromthe fame Points H, Lines to be drawn
to the Point of Diftance, interfecting the Ray A E in O, O, &¢. Perpendiculars
OP, OP, €c. are to be raifed ; then the Plan of this Semi-circle FG is to be
made in fome feparate Place, and the Divifions thereof transferred from E to B.
And fince the Plan of the preceding Figure is equal to F G, take the Divifions of
half of it, BCDEF, and transfer them upon the Perpendiculars AF; and from
the Points EF DCB draw Lines to the Point of Sight D, and through the Inters
fe€tions thefe Rays BCDEF make with the Perpendiculars OP, draw curve
Lines, which will form the Side Arch. Then drawing Parallels through the Inter-
fections 1, 2, 3, 4, 5, 6. 7, 8 9, tothe Divifions of the Arch FG, you will have
Points FRST V XY Z, to form the Crofs after the Manner already mentioned.

-_ For the Thickneffes of the Nerves, or Branches, a litile Line of Elevation
“muft be made, ab, which I have here added at the Top of the Perpendicular
raifed from Q. This Line AB, being drawn to the Point of Sight D, cuts all
the other Perpendiculars in the Point cd, and this gives the proportionate
Heights to each Perpendicular raifed from the Interfeétions of the Crofs, that
is, fron the Interfections made to find the Out-line of the Crofs: The Grit Ele-
vation ab, for Inftance, gives the firft Perpendicular Ge. the fecond Elevation
ed gives the fecond Perpendicular F e; and fo of all the reft in their Order,
which all give Points ¢¢; and-which being connected by : crooked Line, gives
the Thicknefs of the Nerves or Reins of the Vault: As & feen in half the ad-
Joining Figure.

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AVAUL — the ae of the pr -
ceding Rules.

HE feveral Rules already deliver’d fuffice

for the conftru€ting a complete Va uLT,
as that hereto annex’d; excepting for what re-
lates to the Columns, or Impofts, which we {hall
have occafion to fhew hereafter.

PRAGTIGAL, pt

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72 PERSPECTIVE

SB SO oe Bae sel cc Bue xy. OE
a Ete teak Set get raee |

ARCHES andGaTeEs with three Sides.

HE R Eis another Sort of Ceiling which fometimes

i = ferves for a Vault over Doors and Galleries, and even
Churches, having a pretty good Effect in Perfpedtive, and eafy
enough to perform. I have added it here after the Circle, by
teafon it is form’d of aSemi-circle divided into Parts.

Having rais'd the Walls AB, defcribe a Semi-circle includ-
ing the whole Breadth CD; then holding the Compafies
open tothe Width of the Radius E C, and fixing one Point in -
O, with the other ftrike am Arch upwards, cutting the Semi-
circle in G, and another Arch EH from the Point D; then
conne@ing the four Letters CDGH by right Lines, you will
have a Semi-hexagonal Arch. A Semi-circle is likewife to be
drawn upon the Breadth I K, for the Bottom of the Arch;
and to divide it, Lines are to be drawn from the Angles of
the former to the Point of Sight F; between the Interfections
whereof with the Arch, right Lines being drawn, will form
the Arch IL MK, |

An ARCH with five Sides.

“SF THIS Arch is perform’d after the fame manner as the for-
mer; all the Difference lyes in the Divifion of the Circle,
the firft being into three, and this into five. Accordingly the
Semi-circle L M being divided into five Parts.) NO PQ, and
‘ Lines drawn from all thefe Points to the Point R, the reft is
perform’d after the manner already laid down,

PRAGTICAL,

A

EB ROHR ELVA GP EV KRESS BERRY OBI ABYC BIS LHS
Elevations of Round OBjecrTs.

cy HE Defire I have of enabling my Reader to put all
Things in PerfpeGive with the utmoft Eafe, has induc’d
me to fhew how found Figures, as Circles, are to be rais’d of
any Height at Pleafure; and the fame Method may ferve for
all other Rotundo’s, as Cupola’s of Churches, Amphitheatres,
Towers, &c. 7

Having put the Plan of the Round in Perfpective, as alread y
direGted, and rais’d the Line of Elevation A B by the Side there-
of, from the feveral Angles of the Plan, which are here the
feveral Points whereof the Round confifts, o/z.1, 2, 3, 4, 5, 6,
7> 8, 9, &c. Parallels are tobe drawn tothe Line of Elevation,
and Meafures to be raisd thereon as already taught, and thence
transfer'd upon Perpendiculars rais'd from the Points 1, 2, ‘,
4, 5, 6, 7, 8, 9, Be.

The Semi-circle before has but half the Height of that be-
hind, and both the one and the other are mere Out-lines with-
out any Thicknefs, |

There is no round Figure but may be put in Perfpedtive by
this Method ; round Figures, we mean, that are parallel to
the Horizon: For as to fuch as are perpendicular thereto, they
are already taught in the Rules for Vaults.

Behe dette tet tlt dete ttottel iitt tiie te dade] dated di dltot dt deta dee dotted athe

Elevation of PILASTERS.

H E Circle muft be drawn inthe Plan double, as already
ny fhewn in Pag. 29. and between the two circular Lines
muft. be plac'd the Plan of the Parts or Members to be rais’d,
as thofe here mark’d A-B CD, which all tend towards the
Center E; then Perpendiculars to be rais’'d fromall the Angles
of thefe Plans, and their proper Heights fet off from the Line
of Elevation FG; as already fhewn in the preceding Figure,

ccacreiias ebinsteiemabdenehnmemnsaiaihtn tet iaiheiemieinhibnneemeeameenteriencacs 2 a ase ee

aiietteminataemrnineen cr ennaeeea te

73

PRACTICAL

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74 PERSPECTIVE

EA LALAAA DA AAD ADDS AAADAGDSARDASD Abba Dba St ADE RAS SARA LES.
SIG, IC, J, S26, SO FG. LB.SB.2
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FLPEDALHHDLHDHHS HEDLIEDLPHSPHTHPPA PST ITDP GPS DPA POPE DERI DD

AVauurt im form of a Shell,
in Perfpective.

| HIS Figure may ferve for the Follow of a

Church or Grotto, a JVich, or the like :
The Elevation is perform’d after the manner al-
ready directed. — | |

As to the Plat-Band, or Border, A B, which
might ferve for a Cornifh, its Diminution is to be
‘taken on the Line of Elevation in C D, and
transfer’d thence to the Pilafters.

For the Vault, take the firft Arch EF, as be-
fore taught, and in the middle of the Infide de-
{cribe a Semi-circle O, to which draw curve Lines
{pringing from off the Pilafters, and you will
have the Ribs or Reins of the Vault, as in G H
IK. The Heights of the Windows mutt be ta-
ken on the Line of Elevation between L and M.
For the reft, fee the Figure.

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jy

H A VING made the Plan of a double Circle according
: to Pag. 29. and marked the Places and Number of
Pilafters between the two Lines, all of them tending to the
Center A, fet off the Height intended from the Ground to
the Cavity of the Dome, as the Line DE, which is to ferve for
a Bafe Line, upon which the Meafures already laid down on
BC are to be placed; then from the fame Point of Sight G
make another Plan at the Top, like that at Bottom, all the
Places of the Pilafters tending towards the Centre H. To form
the Pilafters all required is todraw Lines from the Places op-
pofite to each other, which will thus give the Breadth and
Thicknefs. I have drawn no Lines for the three Fore Pilafters,
both to thew thofe behind, and to Inftance that there muft
be both at Top and Bottom.

To give the Thicknefs of the Rotundo from I to H, and
from KtoL, fetthe intended Height on the Lineof Elevation
DM, tending to the Horizon in the Point F; and from the
Several Points whereof the Circle confifts, to draw Parallels to
the Line D, whereon are to be erected Perpendiculars, as DM,
which are to be transfer'd thence, with the Compafies, to the
Perpendiculars raifed from the fame Points KL, NO, PQ;
and fo of the reft. :

If inftead of a Round you require a Square, or Polygon,
the fame Method is to be obferved.

PRACTICAL

|
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vi

V 2

76 PERSPECTIVE

co Sees PS Tee
That a Number of OsjEctTs, and Plurality of
STORIES, only admit of one Point of Sight.

:. has already been obferv’d, that one fhould
never ufe above one Point of Sight i ma Pic-
ture, and that the Ignorance of certain Painters
is publifhed to all the World, by their making as
many Points of Sight, sail Horizons, as they
make Lines.

’T is not long fince I remember to have feen a
Painting, wherein there were feveral Rooms one _
over another, each of which had two or three >
Points of Sight; and yet the Pamter took it for |
Miracle. The prefent Figure may ferve to cor-—
re@t this Error, and to fhew, that there fhould |
only be one fingle Point of Sight, to which all/
the Objects, and all the Rooms, tho’ there were
an hundred over or a-fide of one another, are to
tend: As the three Apartments do all hike tend |
to the Point A. The reft is sei as already
directed. i.

PRACTICAL

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a5 PERSPECTIVE

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ETS OIC SOULE MASEL OSUC SIGE

BIG AOS OO: ARE ENT LO) ARM OTA
SES ee ee eee ee ee eee eee SSO SESLES SRE RE LEE ERE

To put CHIMNEYS in Perfpective.

HE Meafures are to be taken on the Bafe Line AB, which, to that End,
muft be divided into equal Parts. The Divifions may be accounted any
Thing at Pleafure. The prefent is divided into eighteen, which we call Feet.

To make a Chimney, or Fire Place; ina Wall, A, three Foot within the
Room, take three Divifions as A, R, C, and from the Point C draw a Line to
the Point of Diftance D, which cutting the Ray AE in the Point F, {gives a
Depth of three Foot. Proceed to fet the Thicknefs of the Jaumb from C, for
Inftance, to G ; then drawing a Line from G to D, it will give the Thicknefs of
the Jaumb inthe Point F. Then fet the Breadth of the Chimney from G to I,
four Foot anda half; and half a Foot, viz. from I to K, for the Thicknefs of
the Jaumb; then drawing Lines from I-and K to the Point of Diftance.D, you
will have their Meafures on the Ray AE, in the Points L.M: And from the four
Points FH LM draw little Parallels to the Bafe Line, as FN, HO, LP,
MQ. Forthe Breadth of the Jaumbs take a Foot anda half, viz. AR, and
the Ray R Ewill cut the little Parallels in the Points NOPQ; from which,
and from FL raife Perpendiculars. For the Height of the Mantle Tree, take
- five Foot on the Bafe Line, and fet them off on the Corner of the Wall from A
to S; and from S to T fet-off for the Cornifh. All the reft is obvious from the
Figure. .

The other Chimney oppofite to the firft is done after the fame Manner: For
thus the Jaumbs are in all Cafes to be managed. And of the Jaumbs may occa-
fionally be made Columns, Termins, or, as wehave here done, Confoles.

To find the Hole, or Aperture of the Chimney, with the Depth of the
Jaumbs, draw a Line from 7 tothe Point of Sight, cutting the Line of Depth in
the Point 5, which will be a Foot and a half; then, from the Point of Diftance
V, draw a Diagonal through 5, cutting the Ray 2 E in the Point 6 ; and from
this Point draw a Parallel, cutting the four Rays 1, 2, 3, 4 in the Points 9, 6,
9, 9: From which Perpendiculars are to be raifed,’ and the reft conducted,
as above.

The fecond Figure reprefents what we have been: fpeaking of, free and .un-
embarrafs’d with Lines. ae

PRACTICAL 77

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78 PERSPECTIVE

fe Cu : fe) le) i ,
CONIC ON OSH OHIO) Ss 1) Oy te

NRBHGDS EE GUNS EO OUSSUSUSSOEO RSS OREOORESEOS

STAIRS in Perfpective.

T HER Eis nothing gives-a Perfpective fo much Grace, or deceives the Eye

foeafily, asa Number of Returns and Breaks; by Reafon thefe introduce
a Number of different Lights and Shadows, which give the Objects fuch a Force,
that they feemed to project or ftand out from the Ground. Now Svairs have this
Advantage, that what Way foever you place them, they have always a Variety
of Shades, and of Confequence are agreeable to the Sight. We fhalladd a few
as Specimens. : 4p Ee oe
- If you make ufe of Squares, there will be the lefs Difficulty,: all required . be-
ing to raife Perpendiculars of as many Squares as you would have Steps; then to
fet the Line of Elevation, divided into any Number of Parts, onthe firft Square,
and from the Divifions to draw Lines to the Point of Sight, which will interfec
the Perpendiculars in the Places where the Steps are to be.

Tis defired, for Inftance, to conftruét a Stair Cafe of eight Steps, the laft of
which to be the Breadth of three of the reft ; take the Number of Squares of
the Plan, beginning at B, and proceeding 1, 2, 3, 4, 5» 6, 7, 8, and allowing
three for the laft marked 11, fromall thefe Angles erect Perpendiculars, to be cut
according to the Divifions on the Line of Elevation BD, in Manner following.

~...%. The firft Divifion, which, fuppofing the Square to bea Foot, is fout Inches

“high, will cut the firft- Perpendicular, and muft be continued to 2, which makes
the Top of the Step; and fo of the reft. The Steps you may make as long as
you pleafe, by fuppofing the Square a Foot: Accordingly thefe here, taking
three Divifions, are three Feet.: Perpendiculars fhould likewifé be raifed, as in
this Inftance, on the Side B: But that Trouble may be faved, by taking the
Height of the Jaft Step H, and that of the firft I, and drawing the Line HI,
raifing the Angleson the Side I, as EK does on the Side B; for this done, you
need only to draw Parallels to the Bafe Line from all the Steps and Divifions of
the Side B, till they interfeét the Line HI in LMNOPQ, Ge. :

One might likewife do without making Squares ; for laying all the Meafures
on the Bafe Line, and drawing Lines from them to the Point of Diftance, the

fame Meafures would be had on the Line A B.
The other Figures we are filent upon, thus much being fufficient for the un-
derftanding and executing them all. oe 4.

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PRACTICAL,

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79 PERSPECTIVE

ocpoo@ov co os ge 0 ac oes co Ss SSIG0IDoe@o

SS

STAIRS open or perforated underneath.

HE Method of managing thefe Stairs is the fame with
that already defcrib’d.
As tothe Aperture, a bare Sight of the Figure is fufficient
to fhew how it is to be put in Perfpective, Thefe two may
give occafion to the inventing many others, 3

fy LOGAN POOL BA GOL SESSOR SSS BOS

STAIRS weewed in Front.

HIS Method is founded on the Ufe of the Line of Ele-
2 vation: As many Perpendiculars are here to be raisd
from the Angles of the Squares of the Plan, as there are re-
quir'd Steps, ex. gr. CDEF ; and from the fame Angles Paral-
tels are to be drawn to the Line of Elevation A, the Interfecti-~
ons whereof give the Points OOOO, from which Perpendi-
culars are to be rais‘d till they cut the occult Rays of the Divi-
Gons of the Line of Elevation. Thefe Meafures are to be taken
in your Compaffes, and fet off on the Perpendiculars rais‘d
( from the Angles of the Plan, each in its Order ; the firft for the
firft Step, the fecond for the fecond, &c.

To find the Returns P P, &c, from the fame Angles P, &e.
Lines are to be drawn to the Point of Diftance Q, and*notice
taken where they cut the Line of the Plan, or the Bottom of
the Step; for Inftance, over the fourth Step is the Plan of the
fifth: Now to find its Return P, from the Point P draw a
Line to Q, and the Point S, wherein it interfeés the Parallel
RR, will be the Line of Return $T; and fo of the reff.

79

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So PERSPECT f VE

Bog BEB x SB OE ei BB ye ERB A.
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Stairs that fhew four Sides.

“H ER E are various Manners of ordering fuch Stairs; two of the eafieft

of them follow. Firft, take the Length of the firft Step, and fet the Num-

ber of Steps required upon the fame ; as on the Line A Bare here fet Points,

€ CCC, for four Steps. From thefe Points draw Rays to the Point of Sight

D, which Rays are tobe cut by the Diagonals A F and BE in the Points I I,

from, which Perpendiculars are to be rais’d, and Parallels drawn to the Line of
Elevation G,. which give the Points H, to be rais’d.as H K.

- On this Line of Elevation G as many equal Parts muft be mark’d as there are
Steps defired, ex. gr. four, here marked 1, 2, 3, 4.. Thefe are all to be drawn to:
the Point D,. to cut the Perpendiculars H. K, and give each its proper Height.
Ehefe Meafures muft be taken in the Compaffes, and transfer’d one after ano-
ther, beginning with the firft G, which is to be fet on the firft Perpendicular
on the Angle A, viz. AL. then a Parallel. to be drawn to the other fide B,
(tho? here we only give half of it, to have room. for the Plan in the other.)
For the fecond Stair the fecond Meafure H 2-is to be taken, and fet off on the
fecond Perpendicular 1; next a Parallel is to.be drawn as before ;. and fo.of the:
reft..

Another Manner.

T EVE Side M N being given, make a Parallel O Pover the fame, for the
Thicknefs or Height of the firft Step: From the two Points O P draw:
two Rays to the Point of Sight Q, and again others to the Points of Diftance
RS which laft will give a Square after the ufual’ Way, and form the firft
Step.. For the fecond, fet the intended Breadth onthe Line OP, ex gr. OT;,.
and from T draw a Line to-the Point of Sight Q:; which Line or Ray TQ.
will cut the Diagonal O: in the Point V, the Place where the fecond Step muft
be rais’d. The Height of this fecond Degree muft be half of V X, asM O:
is half of OT.. The Point ¥ thus gain’d,.a Parallel muft be drawn through
it as far as the Diagonal of the other fide drawn from the Corner Ps. then from ¥
and Z draw Lines to the Points of Sight and Diftance, to form the Square, as:
for the firft Stair. For the third, fet the Meafure V X.on the Line Y Z, ex-
tending, ex. gr. from Y to A 5. and from the Point A draw a Line to the Point
of Sight Q, which interfecting the Diagonal of the Point Y¥, will give the Point.
B for the third Stair. Its Height will be half of B C, which is always that of
© T in Perfpeétive. The reft the fame as in the firft and fecond.

1 ae third: Figure fhews thefe Stairs free of all. the Confufion of Lines and.
Letters. | 4

a0) ROAOTL 1 Cae, 80

——

—

q 5 |
( SEU
= :

85 PERSPECTIVE

CSIR SEE IR TERRIERS CHR GO BE RRIERSARGEGERERABAGAGAGA

STAIRS wew'd fide-wife in Perfpettive.

H E Number of Stairs is firft to be laid down on the Bafe-Line,
that is, fo many Points are to be made at equal Diftance; as in the
prefent Cafe ABC are. From thefe Points Lines are to be drawn to
the Point of Sight D; then fromthe Point A another is to be drawn to _
the Point of Diftance E; which Diagonal AE will give the Plan, and
the Place of the Stairs, by its Interfection with the Rays BC in the
Points I; and by its Interfection with the Ray F, which is the Foot of
the Wall, it will give the Point G, which is the Middle of the Plan of
the Stairs. From G aLine is to be drawn to the other Point of Diftance
H, which gives the Angle of the laft Stair in the Point K, and the Place
of all the reft inthe PointsI I. Laftly, from all the Points I ere Per-
pendiculars.

Now to give the Heights; from the Points A B C on the Bafe-Line
erect little Lines, ferving for a Line of Elevation; on thefe lay the Heights
according to their Number: A, for Inftance, which is the firft, will
only have 1; B, the fecond, will have 2; and C, the third, will have ra
From all thefe Points 1, 2, and 3, draw Lines to the Point of Sight D,
and you will cut the Perpendiculars rais’d from the Plan in the Points O,
which will give the Height of each Step.

That on the other fide fhews the Thing free of Points and Lines. ‘The
fame Method may ferve for divers Purpofes; as for an Altar, a Throne,
the Front of a Church, a Gate, &c.

SESESICO SOC CMS CSCO ICICIONC ICM ACCC CICS E CIC CCOCOO eC

Stairs ma Wall im Perfpective.

AKE as many Divifions at the End of the Bafe-Line as you in-

tend Stairs, as in this Cafe, three between A and B, and from A
and B draw Lines to the Point of Sight C; then, having determin’d
the Space the Stairs are to take up, as DE, a Parallel to the Bafe-Line,
EF, muft be drawn, which in the Points I I will receive the Interfeétions
of Lines drawn from the Points GH to the Point of Sight C; and from
the fame Points II Perpendiculars, IK, IK, are to be ereéted, to re-
ceive the Heights of the Stairs, by drawing Points, 1, 2, 3, to the Point
ef Sight C, as appears from the Figure. 4.

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82 PERSPECTIVE

Al STair-Case with Landing. Places i Per/pettive.

O but recollect the preceding Methods, and you'll find it exceeding eafy to.
conftruct fuch Stair-cafes:: However, to fave the Trouble of too irkfom a
Retrofpeé, we fhall explain the whole here. ;
By reafon Stair-cafes of this Figure ufually run over a Space equal to twice
their Width, to:raife one of them in Perfpeétive, the Horizon mutt firft be dif-
pofed at pleafure ; then a Square to be made according to the common Rules,
and this to be doubled, as direétedin Pag. 16; then divided by an unequal Num-
ber of Squares, that the Wall, which is fuppos’d in the Middle, may be the
Meafure of a ‘Square.
In this Figure each Square has nine Sides, or Squares, on either Hand, which
being doubled, give eighteen ; of thefe, four being left at each End for the
Landing-places, remains ten Squares, or Stairs, each whereof we fuppofe equal
‘to a Foot every way. .
Having left four Squares, beginning at the Point A, which ferves in lieu of
a Wall, ereét a Perpendicular B pretty high, then a fecond C, and a third D;
and fo of the other Angles of the Squares, to the Number of ten. This done
on one fide, the fame muft be repeated on the other; and fuch Perpendiculars
will give the Depths or Breadths of the Steps.
- For the Heights, if they be a Foot broad, they muft be half a Foot high, or
half the little Square A O; which Height being taken in your Compafies, fet it
on the firft Angle, which is to ferve for a Line of Elevation, beginning at the
Bottom, or the Point A, and making as many Divifions thereon as you intend
Stairs, viz. ten, from the Bottom to the firft Landing-place; where you begin
to ae up the oppofite Side, and the Series of Numbers is continued to twen-
ty-three.

Bion all thefe twenty-three Points, Lines are to be drawn to the Point of Sight
_E, and care taken to cut the Perpendiculars in their Order; that is, having laid
your Ruler from the firft Point to the Point of Sight, crofs the firft Perpendicular
B to G with a little Stroke, for the firft Step. For the fecond Step, from the fe-
cond Point draw a Line, croffing the fecond PerpendicularC to D. And fo of
all the reft on both fides. |

From the Angles of all thefe little Strokes between the Perpendiculars draw
Parallels to the Horizon, as far as the Wall F ereéted in the Middle; fuch are
~ the Lines 1111, which I have only added on one fide, to avoid Confufion: ’Tis
thefe Parallels alone that form the Stairs. All the other Lines hitherto drawn
fhould be occult, and not to be feen when the Figure is finifhed.

The Landing-places fhould contain what the laft Perpendiculars come fhort of
the Wall, as from GtoH. Their Height, or Thicknefs, HK, is half a Foot,
the fame as that of a Srair. :

The lower Figure is the fame with.the upper, only that the one has the Ap-
paratus of Lines, Sc, neceflary for the Performance, which the other is without.

PRAOQTICAL,” NG

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FEE ER I I LL LE SOO NN TL IIS ES

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83 PERSPECTIVE

EDEDEDEDENEAD EHEMAVEDEHEMD
ERB EOSEY OMI OSV OMI OS, CSCY OSC OSD OSEY CRD OID,
O30) GOSS OBOS CS

CGIEBEVEgBe

Winding or Spiral STAIRS 7 Perf pective.

N E Side of the Flight, or Afcent, is to be fet onthe Bafe Line, and di-
O vided into as many Parts as you require Stairs: Suppofe, for Inftance,
A Bthe Side of the Stair Cafe, and fixteen Steps required in the whole Circuit of
the Square ; each Side, in this Cafe, will contain four ; confequently AB being
divided into four, a Square is to be formed thereof, divided into fixteen, accord-
ing to the ufual Rules.

From all thefe Divifions, which part the Lines of each Side into four, Per-
pendiculars muft be raifed to give the Bounds of the Stairs. Suppofe then the
Perpendiculars AA, BB, CC, DD, EE; (this E E ftands for three,by Reafon the
Point is in the Middle, and ferves as a Newel, or common Centre of them all ;)
on the firft Perpendicular A, whichisto ferve for a Line of Elevation, the Height
of a StairQ A muft be fet, and from the Point Qa Line be drawn to the Point
of. Sight X, which by its Interfections with the Perpendiculars QRST V, gives
the Dimenfions of all the Stairs. Thus AQ is the Height of the firft, F R of
the fecond, GS of the third, HT of the fourth, andI-V of the fifth. This laft
is the Height of all thofe at the Bottom, as A Q_is of thofe in the Front.

Since GS is the Meafureof the third, which is that in the Middle of the Side,

it mutt likewife be the Meafure of the Centre, and of the Newel of the Flight:
For this Reafon, having taken the Meafure GS in yOur Compaffes, fet. it off in
the Centre of the Square as many Times.as you would have Stairs in the Flight ;
ex. gr. eighteen Times for eighteen Stairs.
’ All Thingsthus difpofed, the reftiseafy. For the firft Step you are to take
the Divifion AQ, and fet it off uponthe Perpendicular D in the PointI, and
from I to draw a Parallel as far asthe other Perpendicular B; then from the two
Points II draw Lines to the third I in the Centre of the Square: Thefe three
III will form the firft Stair. For the fecond, fince its Angle reaches to the
Perpendicular B, which is on the Fore-fide, it muft have the fame Meafure AQ,
which will be 1, 23; then from the Point 2 a Line to be drawn to the Point of
Sight X, cutting the Perpendicular P in the Point2; from which Points 2 and
2 Lines areto be drawn to the 2 in the Centre: Thus will you have formed the
fecond Stair. For thethird, fince it is found on the Perpendicular P, the Mea-
fure F R muft be taken for its Height; and the fame Procefs obferved as in the
former. |

If you would have them round witha], the Square muft be reduced to a Cir-
cle ; according to the preceding Rules: And for the reft, the fame Method will
ferve for both. edie

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84. FERSFBECTEVE

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SQUARES with Circles therein, in Perfpective.

F* H E Method is the fame with that deliver’d among the
Planes. The Circle, for Inftance, is to be divided into
eight Parts, asin Figure A, wherein the Circle of the Front
of the Cube gives the Diminution of that a-Top; and that
in the Front, with that a-Top, the Diminutions of all the
other Sides; as in Figure B, where the Circle is diminithed
on three Sides; and inthe other C, where it is diminifhed on
all three Sides of the Cube.

The three Figures DEF are perforated each on two Sides,
according to the Plan of the Circle A: Thus the Cube D is
pierced thro’ its Fore-fide ; and thro’ that Perforation the
Bottom is feen perforated: Thus alfo E is perforated on the
Sides ; and F thro’ the Top and Bottom, tho’ the latter Per-
foration be not diftinguifhable, by Reafon the Matter is not
fuppofed tranfparent. :

The three Figures underneath reprefent the Pieces cut out
of each Cube; G, for Inftance, out of the Cube D, H out
of E, and 1 out of F. -

Upon the whole, the Method of difpofing fquare Figures
in Circles appears very eafy; nor can the Reader find any
Difficulty in placing Columns under any Difpofition at all,
The Reafon why we have given none before is, that we
chofe to render the taking of Elevations as eafy to conceive,
and the Practice as little embarraf{s'd as poflible. Thus much
may ferve for the Beginning of Columns; how to carry on

and finifh them. fhall be fhewn hereafter. 4

PRACTICAL, i

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8c PERSPECTIVE

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BDOKGRIODO ABH IDOKRNOCSI KRHOD’ HRRMOSSE ROSS

Rounp Stairs 7 Perfpective.
7 O raife thefe three round Stairs or Steps, in

a front View, make a Plan of three Circles
within each other, after the Manner already di-
rected in Pag. 28. and from the feveral Points
that form the Circle draw Lines parallel to the
Bafe, as far as the Ray A, which is the Foot of
the tine of Elevation A B: This gives the Ele-
vations, which are to be taken thence with the
Compaffes, and fet off on Perpendiculars raifed
from the feveral Points of the Plan.

Rounp STEPs wiewd Side-wife.

H E Rules for Objects viewed by the Sides
| we have often obferved are the fame with

thofe for Obje&ts in Front: However, to fhew
‘we are not always obliged to obferve the Divifion
of the Circle into fixteen, thefe of the Side-view
we have divided into eight. For the refi, *tis the
- fame as in the preceding Cafes. The Lie of Ele-
_ vation 1s CD, drawn to. the Point of ‘om E.

PRACTICAL 5:

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86 PERSPECTIVE

Bey eee owSs errr $ ones - ee tre

WiINDING-STAIRS.

HIS Figure is the fame with the preceding one, which

was not fhaded, that the Method of the Operation
might be the more confpicuous: For the fame Reafon the
Newel of the Stair-cafe was referved for this Figure. It is form-
ed by affuming the Point A as a Center, and thence defcribing
a Circle; or rather a Semi-circle, as BC,. by Reafon only half
of it is to be feen. To the Center of this Semi-circle Lines
muft be drawn from all the Divifions of the Square of the
-firft Plan, as DEF GHIK, which will cut the Arch BC in-
tocight Parts; and from the Interfections OO, &c. Perpen-
diculars are to be raifed ; taking Care they cut precifely in the

Points, where the Steps are placed ; the Step I, for Inftance,
to becut by the Perpendicular raifed from its Point in the
Semi-circle, asin A; the fecond Step to be cut by the Perpen-
dicular raifed from the Point which K gives in the Semi-circle :
And fo of the reft.

The Doors, Windows, &c. in the Figure, are all con-
ftructed according tothe Rules already laid down.

PRACTICAL 86

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PERSPECT. IY E

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LOS Ee AR Se SS eS

CoLtumNns i Perfpective.

W H A T has been juft obferved is not confined to the Cube, but ex-
tends equally to any Thing intended to be rounded. For Inftance,
if from the Square, A, you would raife a round Piece, AB, defcribe a
Circle within the Square, according to the common Rules; and at the in-
tended Height defcribe another Square, with a Circle within it, B. Now
to get the two Lines DE, which make the Thicknefs, or Diameter of
the Circle, obferve where the Circle cuts the Diagonal of the Square, and:
take thofe Points for the Lines which form the Sides of the Elevation..
Thus C is formed by Perpendiculars raifed from the Interfections DE of the.
Circle with the Diagonal of the Square.

Thus much Regards Side-views. Asto thofe in Front, ex. gr. the Fi-
gure F, they are always to take up the Semi-cirele GHJ, and Perpen-
diculars are to be raifed from the Extremes of the Diameter GH; and
both in thofe in Front, and thofe in Side-views, Perpendiculars to be raisd:
from the Center, to give the Diminutions..

As to the three Figures underneath, befide that they fhew the former
more clearly, and with the Addition of Shadowing, they likewife ferve to
point out the Manner of proceeding for Columns, The middle Figure, K,
is quite round, without any Ornament at all. The fecond, marked L,
fhews, that when a Bafe is required, a double Circle muft be defcribed:
on the Square that ferves as a{Plinth, whofe upper Part is MN; the In--
terval between the Circles to be the Projeture of the Bafe, and the inner.
Circle the Plan of the Bafe, from which Perpendiculars are to be raifed.

The third Figure, O, is a Column with its Ornaments; which every
one is to make at his Difcretion;, taking Care the Abacus anf{wer, as it ought,,
to the Plinth. 2.

87

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88 PERSPECTIVE
Sp SedeT EBB Te TRE BR MERLE

Cornicesand Mov.opines ia Perfpettive.

FT ER the Columns, which ate the chief Ornaments of Architecture, we
proceed to the Cornices, or Mouldings, with their Projectures ; which have
hitherto been omitted, for Fear of rendering our Elevations perplexed. )
>Tis certain there is fcarce any Building but has fome Moulding or Projecture
by way of Enrichment, and to render it pleafing to the Eye; for this Reafon we
have here judged proper to add what relates thereto: Not, we mean, to the Con-
{truétion thereof, for that depends on every one’s Fancy nor to the Meafures
and Proportions, for in that Cafe we fhould be obliged to give all the Orders of
Architecture, and a Thoufand other Things, which the Reader will find elfe-
where: But to put them in Perfpedtive, when any particular Order is pitched
upon.

To put the Ornaments, for Inftance, of a Pilafter in Perfpective, take the
Proportions from the Profile of fome other, with all the Ornaments thereof, as
AB; whofe Breadth being taken, and a fquare Plan made as ufual, erect Per-
pendiculars from all the Angles thereof: Thus will you have the Body, or Shaft,
of the Pilafter.

Proceed now to take the ProjeCtures, or Jettings ew. gr. the Bafe of the Pilafter
C, and the feveral Meafures thereof lay: down inDE. To put this in Perfpec-
tive all round the Pilafter, from the Point of Diftance F draw a Diagonal to the
Point E, and farther at Random, astoG; then from A draw a Line to the Bot-
tom of the Projecture H, and in the Point I, where this cuts the Diagonal, will
be the Jet, or Projeéture, of the whole Bafe. The fame Line AH gives the
Projeture of the Bottom, by its Interfection with the other Diagonal in K.
For the Projeéture of the Front, from the Point I draw a Parallel to the Bafe
‘Line, till it cuts the Diagonal in LL: This gives the other Corner of the Projec-
ture of the Front. Then drawing Lines from the Top of the Bafe to thefe
Points, as from M to L, and from N to K, you will have the Breadth and
Height of the whole Bafe. The fame Method ferves for the Capital.

The Figures underneath fhew the reft ; and even the Effeét of what is faid,
free of Confufion. For the Pilafter O, Regard muft be had to that above it, P,
where the Line DH has upon it all the Interfections of the Bafe, For this
Reafon Lines are to be drawn from the Point of Sight A, which paffing through
the Divifions of DH, will exprefs the fame on the Lines DI and NK; then
Parallels being drawn from the Points DI to ML, nothing remains but to draw
the Out-Lines. When there happen Squares, or Fillets, either at Top or Bot-
tom, they are formed by Perpendiculars. ‘Thus, for the Plinth, Perpendiculars
muft be raifed from the Points LIK, and fromthe Point of Sight A a Line to
be drawn through the Angle of the Plinth to Q’s this will give the Height of the
Perpendiculars land K. Liaftly, L isto be made equal to I.

This Inftru€tion for the Bafe will fuffice for the Capitals ; the Operation being
the famein both. The Jaft Pilafter, R, is only meant to fhew one clear of Lines.
They are all broke in the Middle, that there might be Room to exprefs both the
Bafe, and the Capital ; the Page not allowing them to be reprefented whole.

PRB aE © ge

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89 PERSPECTIVE

EELS ESSE EEE S SSS EEL EE EES EEE E EOE EEE PEE ee PE EEE EE PELE h Et

(OG ORIG Oe Fe IG Oe Fe

PEPPPPPAPPPHSHAF PEDEDEALERAASLASDADPALED HHS SSAA SSIS H EAH}

A large Cornice above the Horizon, in Per/pective.

HE Method is the fame as that juft delivered; but being fomewhat trou-
blefom by Reafon of the Number of Lines, we have judged proper to re-
peat it again here, inorder to avoid Confufion.

To the Purpofe then: Having taken the Profile of the Cornice, and its Pro-
jecture, you are to transfer itto the Place where the Draught 1s to be made;
as here the Profile C, €Sc. is at the Corner of a Wall AB. To find what Height
it mufthave, and to make it thew its Bottom, from the Point of Sight D drawa
Line through the Extreme of the Profile E, as the Line DF ; then drawa Dia-
gonal from the Point of Diftance H, paffing through the Corner of the Wall B,
and prolonged till it cut the Ray DE in the Point F ; from which draw the Line
FG, which is to reprefent the Angle in Perfpective, and to receive all the Mea-
{ures of E.G. The Corner of the other End of the Wall, KL, is to be drawn
to the Point of Diftance I, as being the other Diagonal. :

In Fig. Il. it is fhewn, that all the Figures which are on the Line MN, are to
be transfer’d, by Means of vifual Rays drawn from the Point of Sight D, upon
the Line NO; in order for Parallels to be drawn through all thofe Points, which
are to give-the Cornice complete. But before we go farther, it is to be obferved,
as has been already hinted, that all Plat-bands and Squares are formed by Per-
pendiculars. Thus, forInftance, to form the large Square of the Cornice, having
made the Doucine, and the Fillet; from the Bottom of the Fillet, which is the
Top of the Square, let fall the Perpendicular PQ: Then, to find the Place it is
to be cutin, to fhew the Bottom, a Line muft be drawn from the Point of Di-
flancel, through the Point a-top of the Quarter Round R, to the Perpendicu-
lar PQ); and you will have your Defire. What. has been faid of the large
Square, holds equally of the leffer ones; as the Denticles, Fillets, &%c. which
are all to fhew their Bottom.

‘The third Figure fhews, that having found all the Points, and drawn Lines on
the Line of the Angle, ST, propostional Mouldings muft be drawn thereon.
I mean, that when they projet much, as is here the Cafe, by Reafon the Point
of Diftance is near, the Mouldings muft be helped out a little ; that is, the
Quarter Round mutt be inclined a little, the Doucine be erected, the Fillets en-
larged ; andthe famedone at one End as the other; ex. gr. the fame on V X as on
ST. This done, all that remains, is, to draw Parallels to. the Bafe Line.

The fourth Figure is the Cornice complete. In this we have drawn Parallels
from all the Points of the Line of the Angle Y Z; and one End of the Wall is
made to pafs over the Cornice, to fhew, that we are at Liberty in fuch Matters ;
and that the Rule is general.

PRACTICAL

89

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To find the Bottoms of /arge PROJECTURES.

i O find the Projecture of the Corona of the Wall A;
on the Angle of the Quarter Round B, make a Line
equal tothe Length of the intended Projefture, as BC; then
from the Point of Sight D, draw a Ray E, pafling to the Ex-
treme of the Meafure GC: This done, draw a Diagonal from
the Point of Diftance F, pafling through the Quarter Round
B; and the Point G, wherein it interfects the Ray DFE, will
give the Bottom on both Sides, BH: As is more clearly ex-
prefs'd in the oppofite Figure K. |

The Projecture of the Wall L, is formed after the fame
manner as the former, A. All the Difference is, the Projec-
ture MN, of the Wall L, is half as big again as that of BC;
to intimate, that the fame Rule makes them as big, or as lit-
tle as one pleafes.

"Tis likewife obfervable in the fame Wall L, how the Return
of the Projecture, &c. is found. For Inftance, from the
Point O of the Quarter Round in the Fund of the Wall, a
Diagonal is drawn to the Point of Diftance P; and the Inter-
{e&tion of that Line with the Ray ED will be a Point, through
which a little Parallel tothe Horizon RQ being drawn, will
give the Thing required. :

The fame may ferve for all Squares on Cornices and Mould-
ings both great and {mall.

The Wall S, thews all the Mouldings on that of L, more
diftinaly. | 2

LPRAGTICAL.

—————

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93 PERSPECTIVE
The Apertures of Doors in Perfpeétive.

AVING hitherto kept pretty clofe to the Order obferv’d in the actual

H raifing of Buildings of all kinds, we now proceed to fhew how to furnifh
nd difpofe them for the Reception of Guetts. We begin with wooden Doors;
hereafter we fhall find occafion to fpeak of other Apertures, as Windows,
Cupboards, €c, then of Moveables, as Tables, Beds, Chairs, Chefts, Benches, &c.
All Doors made to open and fhut depend on the Pleafure of the Perfon who
may open them as far and as little as he pleafes. For this reafon I fhall thew a
Method of putting them in Perfpective, at any Degree of Widenefs at Difcretion.
Now it is obfervable, that Doors, Windows, Cabinets, ‘Chefts, and, in fine,
all Things intended to open and fhut, always defcribe a Semi-circle in opening.
The reafon is, that the Side hung by Hinges keeps its Place, like the fx’d Leg
of a Pair of Compaffes, while the other Side, like the other Leg of the Com-
pafies, {weeps its Arch. Thus in the Plan underneath the Figure, the fix’d Side

being at A, and the other at B, if you open the Door quite, the Side B muft -

defcribe the Semi-circle BCD, whofe Centre is A. Hence it follows, that if
the Door be three Feet broad, as in the prefent Cafe, its Semi-diameter A C
will likewife be three Feet, and its whole Diameter B A D fix Feet. Of thefe
fix Feet in Length, and three in Breadth, a Plan muft be made, confifting of
eighteen Squares, wherein a Semi-circle A BCD is to be defcrib’d, to render
the making of the fame Semi-circles in Perfpective the more eafy: Always ob-
ferving where the Semi-circle of the Plan cuts the Squares ; that thofe in the
Perfpective may be cut after the fame manner, and a Semi-circle be drawn, taking.
up the fame Space, traverfing as many Squares, and cutting them in the fame
Places. An Inftance of which we have in the Door E, where the Interfections
are mark’d the fame as inthe Plan underneath, 1, 2, 35 45 5> aa

When a Door is to be reprefented open, in Perfpective, a Semi-circle mutt be
ftruck on its Plan, and the Point of Aperture placed on any part thereof at plea-
fare: Thus for-the Door E the Point of Aperture is fix’d at 2. From this Point

2 a Perpendicular muft be rais’\d, 2 H; and from the fame Point 2, a Line muft —

be drawn through the Corner. of the Door F, and continued till it cut the Ho-
rizon in the Point G ; from which another Line muft be drawn through the other
Corner of the Door I, and continued till it cut the Perpendicular rais’d from
the Point 2, in the Point H: Thus will you have the Door open, F I H 2.

All Apertures are perform’d by the fame Rules; as is farther feen inthe Doors
K and L. The Door K fhews its Out-fide, and that of L its Infide; yet both
are perform’d after the fame manner as the firft. The accidental Point of K is
the Point M inthe Horizon, and that of the Door L is O. If Bolts, Locks, or the
like, be added on the Doors, they muft all be drawn from the fame acciden-
tal Point; as the Bolts and Lock of L tend -towards O. What accidental
Points are, we have already explain’d. Now all Apertures have one fuch Point
in the Horizon, excepting two forts : The firft, when the Door is quite open ;
in which Cafe its accidental Point is the Point of Sight : The other, when ’tis pa-
rallel-to the Horizon 5 by reafon the Parallels, in that Cafe, never intericct : as
in the Door N. | 2

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Cornices with feveral Returns.

H EN there happen divers Turns and

Returns in the Cornices or Mouldings,
their Bottoms muft always be taken from the |
Points of Diftance. . Thus, having drawn Rays,
A and B, to the Point of Sight E ; from the Point
of Diftance C, or D, a Diagonal muft be drawn
through the Angle of the Quarter Round O, till
it cut the Ray A or BinI: From which Point, I,
a Parallel to the Bafe being drawn, gives the Bot-
tom or Projecture of the Square; as already
{hewn in Pag. go.

I would willingly have made a much bigger
Cornice; as that would not have been a whit the
more difficult: But the Compafs of the Page ob-
lio’d me to be contented with this.

If you would have Returns on the Ground, as
thefe are above the Horizon; the fame Method
‘sto be obferv’d. For Proof of this, imvert the
Paper, and you'll find it have the fame Effect.

PRACTICAL 92

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Cornices avd Moutpincs below the Horizon.

HE Rules that obtain here are the fame with thofe of

the preceding Cafes ; tho’, through an Accident which

fometimes falls out, viz. a Diverfity of Horizons, there arifes

a little Variation; which fuch as are unacquainted therewith
might chance to be puzzled withal.

We obferve, then, that in viewing a Cornice below the Eye,
and of confequence below the Horizon, the Proje@ures hide
fometimes half, fometimes more, and fometimes lefs of the
Body, according as the Eye is more or lefs elevated.

To find precifely how muchis to becovered, and how much
not; fet the Profile of the Moulding on the Corner of the
Body to be enrich’d therewith; and having found the Line of
the Angle, after the manner already directed, draw the Divi-
fions of the Profile upon the fame: Thus will you find that
the Square, or Plat-band, covers the whole Aftragal under-
neath, and only lets half the Fillet be feen. For, drawing a
Line from the Point of Sight A, through the Profile B C, it
cuts the Perpendicular from the Line of the Angle in D, and
fhews how muchis to be cover’d. For the Moulding at Bot-
tom the fame Method ferves as for that at Top.

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AperTURES of Cafements in Per/peétive.

A LL the Difference between the Apertures of Cafements, and thofe of Doors,
| lyes in this, that Doors have their Semi-circle of Aperture on the Plan,
and Cafements in the Air; by reafon Windows are rais’d, and Doors ufually turn
onthe Ground. On this Account, the Semi-circles of Cafements may be either
over or underneath them: And in fuch Semi-circles is the Point of Aperture ta
be placed. |
hus, for Inftance, if a Cafement be two Squares, or Panes, broad, as A B,
and it be made quite open, it will then take up two Squares more C A, whereof
A is the Middle, and the Centre of the Semi-circle A BC. But by reafon the
Window 1s rais’d above the Ground, the Semi-circle muft alfo be rais’d ; as is
here actually done in the Semi-circles of the Windows D and E:: whereof the
fame D, and Eare the Centers ; and which are eafily form’d by ereéting Perpen-
diculars from the intermediate Squares, till fuch time as they interfeét the Rays
drawn from the Corners of the Cafements D, E. From thefe Interfeétions Lines
muft be drawn to the Bafe-line, and the Meafures of the Squares of the Plan
1, 2, 3, be fet thereon. From the fame Points 1, 2, 3, Lines are to be drawn to
the Point of Sight F; which cutting the Parallels, will give Squares to fix the
Aperture by. Proceed then to take the Apertures: after the fame manner as
thofe of Doors. For Example, the Point G being given in the upper Semi-circle,
from the fame G, draw two Lines ; the one, G H, perpendicular; the other’
paffing through theCorner of the Window E, and cutting the Horizon in fome:
Point, ¢. gr. the Point I. From this I, draw a Line through the Corner of the
Window K, till itcut the Perpendicular in the Point H, which gives the Cafement
open, K EG H. The fame is to be obferv'd with regard to all the reft ; and the
Point fil] to be‘taken in the Horizon. Thus, L. isthe Point for the Cafement M ;
and N, that for the Cafement O. The Cafement P has none at all, as being
parallel to the Horizon.

The Cafements on the other fide are perform’d after the fame Method, with-
out any of the Confufion of Lines... Both the one and the other range with the
_ Wall, to facilitate the Operation. The Door at Bottom is done after the man-
ner already directed; and the Cafement according to the Method laft deliver’d.

Apertures of Cafements, with Embrafures.

: ee E Rules for thefe are the fame as for thofe that range even with the
Wall; excepting that the former are not capable of being quite open’d, by
reafon of the Thicknefs of the Chamfraining, or Embrafure. On this account we
never give them a whole Semi-circle,’ but a Portion anfwerable to the Aperture
they admit of. The accidental Point fhould always be in the Horizon, for upper
Windows, as here in QandR; that below is parallel to the Horizon. ;

an OTT CAT. 94.

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95 PERSPECTIVE

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Divers other APERTURES.

T HIE Openings of Cupboards, Preffes and Chefts, are at leaft as neceflary as
thofe of Doors and Windows; nor had the Omiffion of thofe been a whit
more excufable than of thefe. Their Doétrine will be difpatched in two. Figures.

The Cupboards A A, are opened according to the Rules delivered for Cafe-
ments, which it would be needlefs here to repeat. We fhall only add, that the
uppermoft is parallel to the Horizon; and that the latter tends to the Point of
Diftance B.

Thé Shop on the other Side is opened by two Leaves, one of them rifing up-
wards, and the other falling downwards. Each of them defcribes its Semi-circle
from the Centres C and D ; which being drawn with the Compafies, the Aper-
tures are fixed at any Point at Pleafure; as here in the Point E; from which a
Ray is drawn to the Point of Sight F, till ic interfeét the Semi-circles at the other
Ends in the Points G. From thefe Points E and G Lines being drawn to the
Centres CD, give the Leaves that clofe the Shop. :

In the lower Figure there are three Chefs, differently opened. ‘To open the
firft, Hy, the Quadrant M is put in Perfpective, according to the Meafures of
the Squares of the Plan. Thus, obferving the Width of the Cheft, which is two
Squares, Perpendiculars are to be raifed thence, and a Semi-circle, or Quadrant,
defcribed for the Opening, which is here fixed at the Point N; and from this a
Parallel is to be drawn to the other Quadrant O ; and from N and O Lines to
be drawn to the Center P. If a greater Aperture is required ; a Semi-circle to

be drawn in Lieu of a Quadrant.
"The Cheft 1 has the eafieft of all Openings: For, having taken the Breadth of
the Cheft QR, from the Centre R defcribe the Semi-circle QS; then take
any Aperture at Pleafure, as T, and draw a Line to the Point of Sight V, cut-
ting the other Semi-circle in X; and, laftly, from the Points T and X,. draw.
Lines to the CornersR. : :

If *tis required to open them farther, you have only to fix the Point of Aper-
ture higher in the Semi-circle; as ¥ is in the Cheft K. The reft is the fame as
in the firft Cheft.

PRACTICA L: Q5

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PERSPECTIVE

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VO? CICOGIES GIG

Plans avd firft Elevations of Moveables.

aie EIESE Plans I thould have placed in their order among the reft, but for
this Confideration ; that had I treated of them at the Beginning of the
Work, without fhewing the Neceffity thereof, they would have paffed for ufe-
lefs, and accordingly have readily dropt out of Remembrance. They now come
in Seafon, and cannot fail of being well received and learnt with Pleafure; inaf-
much as there are no Moveables or Houfbold Goods but depend upon them,

The firft Plan, A, may ferve for Beds, Tables, Chairs, Stools, 8c. The other
B, which is twice as long as ’tis broad, ferves for long Tables, Cupboards, Buffets,
Chefts, Trunks, &c. The third, C, which is long and narrow, ferves for Benches
or Forms, Couches, and other Things with fix Feet. :

The Acquaintance the Reader is fuppofed to have with the other Plans already
delivered, will render the Performance of thefe eafy 5 there being nothing more
required than to lay down their Dimenfions on the Bafe Line, draw Lines thence
to the Point of View, and fhorten them by Means of the Points of Diftances.

Thus, e. gr. for the firft Plan A the two Meafures of A and D mutt be fet
on the Bafe, and Lines be drawn thence to the Point of Sight F. Then from
one of the Points of Diftance, a Line to be drawn to one of thofe Meafures, as
from G toE; and through the Points H, and I, wherein it interfects the Rays,
Parallels to be drawn; by this Means four Squares will be formed, which you
may account as much or as little as you pleafe.. Fora Table, ¢. gr. they muft be
more than for a Stool, 7. ¢. they muft have more Breadth ; the latter being ufual-
ly two Inches, and the former four.

The Plan B is performed after the fame Manner; excepting that on Account
of its Length, which is double its Breadth, a Line muft be drawn from B to one
of the Points of Diftance, to find the half, K. For, if a Line were drawn from
L,, it would interfe&t in M, and givea whole Square; whereas we only want half
of it. Parallels then muft be drawn from K to the Points of Interfection with the
Ray ; and from the Corner L, a Line muft likewife be drawn to G, interfecting
the Ray: Thus will you have the-firft four Squares.

The third Plan, O, needs no Explanation; it being evident that it is formed
like the firft, A; and that the Square muft be doubled to get the fix little
Squares. ee

4p rom the Figures underneath it appears that Perpendiculars are to be raifed
from all the Angles of thefé Squares, to begin to form the Moveables, &¢, laid

down hereafter. 3

PRACTICAL

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97 PERSPECTIVE

(BRR CRI KAT LEYTE Ls OOH ALT EIB EI CI
ELEVATIONS of Moveables.

A VING raifed Perpendiculars from the Plan, as already intimated ;
a Line of Elevation muft be made in fome Part of the Painting, on
which the Heights, crofs Pieces, &c. are to be laid.

Thus the Line CD being a Line of Elevation, and CE and DF
Breadths or Depths of the crofs Pieces; from thefe four Points draw
Lines to fome Place in the Horizon, ex. gr. the Point G. Then having
erected Perpendiculars from all the Angles of the Plan, as in A andB;
from the Angles draw Parallels to the Bafe Line, till they cut the Line
CG: Thus will you have the Points 1, 2, 3, 4.; from which Perpendiculars
are to be raifed. And the Interfections thofe Perpendiculars make with the
Ray CE, will be the Points to cut the Perpendiculars of the Plans: Whe-
ther. they be transferred with the Compaffes; or whether they be cut by
Parallels, as inthe Figure ; where a Parallel being drawn from the Point
E, cuts the firft Perpendiculars of the Plans AB in the Points O; from
which drawing Lines to the Point of Sight H, the other Perpendiculars
of the Plans will be cut in the Points PP, &c. And doing the like for
the Point F, you will at Length have a Cube perforated on all its Sides:
Which being well underftood, all the other Pieces that follow, and even
all that can be conceived, will be readily performed.

It is eafily obferved, that the two Frames or Stands of Tables, I and
'_K, are performed by the fame Rule. as thofe above: All the Difference is
in the Crofs-bar at Bottom, which is higher in the Line of Elevation in
this latter Cafe, thanthe former. Inthe latter, for Inftance, we find it in
the Line L, which gives MM. For what is beneath; one may either
leave the Feet {quare, or round them into Bowls.

As tothe laft Frames, N and Q, there is nothing in them more than in
I andK; only that they are viewed by the Angle, and the other in Front.
The Plans of thofe, I and K, are drawn to the Point of Sghe R; and
thefe latter to the Points of Diftance S, T.

Thefe Figures furnifh wherewithal to form all the Moveadles of a Me-
nage. Thus, for Inftance, to make a Bedftead of Fig. I 0: K, nothing
more is required than to give it a proper Height and Breadh, In every -
Thing elfe the Operation is the fame as for a Couch, a Stool, or the like:
Fora Table you have only a Top to add: Fora Joint-ftool, bide the Top,
it muft be made more in Height than Width. But the ret is all of a-
piece. : 3

.

PRACTICAL

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98 PERSPECTIVE

BES 0 Oa CH eG Boxe se LOB oe iE Bex OS BE
Bes Ste ce Seep Gene = ce Bp RGR ca

To make the upper Part of ‘Vables, Stools, &?c.

Haye G raifed Perpendiculars from the Plan, as al-
ready directed, and fix’d the proper Height thereon,
the Frame will be complete. Now to make an upper Part
perfe@tly ona level, and which thall not exceed the Frame,
there needs nothing more than to leave the Top of the Cube as
it is) without exprefling any Thing thereon; which will make
the upper Part of a Table, Stool, or the like.

But if ’tis defired the upper Part hall have a Projecture, or
Ledge ; from one of the Angles of the Frame a Parallel muft
be drawn, as AB; and on this Parallel the Meafure or Quan-
tity of the intended Projecture mutt be fet, as here AB. Then

from the Points of Diftance CandD, occult Lines, AE, AE,
©’c. muft be drawn through the Angles of the Square of the
Frame here exprefled by dotted Lines. And to make the
Meafure A B give the proper Breadth toall the Sides and An-
gles of the Table; draw a Line from the Point of Sight F,
thro’ the Point B, continuing it till it cut the Line CAE in the
Point G, Fromthe Point G draw another Parallel, cutting the
other occult Line in H. Then drawing Lines from the Points
Gand H to the Point of Sight F, the other Diagonals will be
interfected in I and K; which will give the upper Part of the
Table, with the Projeture firft fet on the Line A B,

The Thicknefs of this upper Part of the Table is fixed at
Pleafure. |

This fame Method may ferve for the upper Parts of any
Thing, whether above or below the Horizon; or whether in
Front or in Side Views.

PR AC T1 CAL, 98

ib “ J
|

99 PERSPECTIVE

By 3 BO x Bn On e SRB x BOs
SS CBO GEES * GOB ™ ee GOST * *BSN™ NOSSO ™ ee?
BDO WOASO GROCER SD KRHOOCK NOIR OK

Elevation of Buffets, and Cup-boards.

A VING made the Plan, and raifed Perpendiculars from all the

Angles, as already taught ; upon the Line A B, which is here to
ferve fora Line of Elevation, the Meafures or Proportions of the Diftances
of the Shelves, with their Thicknefles, &c. as here CDE, mutt be laid
down. Then from the Points CDE, draw Parallels to the Bafe Line, as
faras the upright Poft GF; and from the Points thus mark’d on GF,
draw Lines tothe Point of Sight H, as far as the other Poft IK, forming
the Breadth of the Buffet. This Breadth is fixed at Pleafure, by laying
down the intended Meafure on the Bafe Line. Thus for the Breadth of
the prefent Buffet, the Diftance F L is laid down ; and from the Point L,
a Line is drawn to the Point of Diftance M; and the Point], wherein it
interfeéts the Ray F H, is the Place of the laft Poft.

The Buffet on the oppofite Side is performed after the fame Manner.
Toadjuft the Proportions of the little Cabinet, or Locker, fupported by
two Columns in the Middle thereof, take the Points L P, which are in the
Middle of QIN, or of the Breadth of the Buffet ; and drawing Lines thence
to the Point of Diftance O, where the Ray NH is interfected thereby,
draw Parallels to the Bafe Line, cutting the Ray TH in the Points VV,
And Perpendiculars raifed from thofe Points will give the little Cabinet in
the Middle. .

The large Preffes, or Cup-boards, in Fig. Il, are performed after the
fame Manner as the Buffetsabove; only that in the Middle needs a little
Explanation, by Reafon it is viewed in Front, fo that there might be fome
Difficulty in determining its Depth. We obferve, then, that its Plan
mutt be formed, as already dire€ted, and as one half is here fhewn.
Then, to make crofs Pieces equal to thefe in the Front, occult Lines
muft be drawn from the firft upright Poft R, to the firft Perpendicular
of the Depth §; and from the Points of Interfection draw little Parallels
to the Bafe: Thefe give the Thing required, 2

PRAG BICAL. 99

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ELEVATIONS of Chairs.

O raife a Chair; fromthe Dimenfions ABC, erect Per-
endiculars, wad proceed in the fame Method already
directed for Table-Feet, or Frames without Tops. All that
is here farther, is the Back of the Chair; which may be made
of any Height at Pleafure. Inthe prefent Cafe the Height of
the Back is equal to that from the Foot A to the Seat K.
Which Proportion may ferve equally for Elbow Chairs.

From the Figure it appears evident enough, that, to form
the Back, there is nothing needed but to prolong the Perpen-
diculars of the Legs, as here AE; and from the Point E to
draw aLine to the Pointof SightG; which cutting the Poft
raifed from the Plan, or the Foot H gives the Point F. The
reft the Figure makes clear.

If Elbows are required, you have only to prolong the Fore-
Feet or Pofts, as the Hind-ones are for the Back: And to
draw a crofs Piece, or Bar, as LM, for an Elbow.

Inthe fecond Figure underneath, you feea Form, or Bench,
-coverd with Cloth, and two Couches, The Head of one of

which is turn’d thiis Way, and the other viewd obliquely. It
would be Lofs of Time to dwell upon the Mannerof makin,
them; the Rules being altogether the fame as thofe already

laid down for other Moveables, viz. by makingaPlan, raifing
Perpendiculars, &e.

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101 PERSPECTIVE

Another Method of putting Moveables iv Perfpective.

HERE are fome Moveables that-fold, or {hut down, and
that ferve for Tables, Seats, Beds, © c. very eafy to
put in Perfpective. te

As to the Elevation, it is perform’d as that of a Cube, as
fhewnin A BCD, which is view’d in Front; or EF GH. Then
two Diagonals, AC and BD, are to be made for that in the
Middle of the Front; or EH, and FG for that of the Side:
And thefe will ferve for the drawing of the two Croffes; tak-
ing Care that one enter half through the other, as GK does
through HI; and both of them to be faftened by the Middle
to make them fold.

In the Figure underneath we add a Table upon Treffels, that
even the leaft confiderable Moveable might not be wanting. To
put them in Perfpeétive, from the Points A, B, which are the In-
terval between the Feet of the Treffels, draw a Line to the
Point of Sight C; then, laying down the Thicknefs of the
fame Feet on the Bafe Line, as here D and E, draw Lines from
the fame to the Point of Diftance F, and obferve where they
interfec&t the Ray BC} and from the Points of Interfection draw
little Parallels to the Bafe Line ; by which you will have the lit-
tle Squares or Plans of the Feet, asin Aand B: Then between
the Diftance D and E, lay down the Breadth intended for the
Top of the Treffel, and drawing ‘a Line thence to the Point
B,. it will cut the Ray BC inthe Points G and H; from which
Points, Perpendiculars are tobe raifed. to any Height at Plea-
fure, as here to I. Laftly, from the Angles of the little
Squares of the Plan draw Lines to I. The fecond Treffel is
performed after the fame Manner as the firft. :

The Form K, and the TZad/e, or Seat L, need not any Ex-
planation, to put them in Pradtice, as having mothing but
what iscommon with the Pieces above-mentiord.

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aced without any Order.

MOVEABLES fi
HEN Moveables are placed orderly along the Side of a Wall, or
in the Direction of the Rays and the Bafe Line, ’tis eafy to put
them in Perfpeétive by the Rules already delivered: But if they be irre-
gularly placed, as in this Figure, you are to proceed as we fhall now
direct. Draw the geometrical Plans, R, S, and T, for Plans of three
Chairs; which are to be diminifhed by the Rule already delivered for the
irregular Figure, Pag. 40. and the- Plans will be found fituated like the
Chairs, or rather the Chairs like the Plans. Now the Plans being in
Perfpective, lay a Ruler along one of the Sides, to fee. what accidental
Point it gives in the Horizon; thus, laying a Ruler along the Side AB,
we have the Point C in the Horizon for an accidental Point, to which all
the Lines of that and the oppofite Side muft be drawn: Thus we fee that
Aand D are drawn tothefame Point C. ’Tis true each Plan placed irre-
gularly fhould have two accidental Points; but they are frequently fo far
off in the Horizon, that ’tis a Chance you don’t find them both. The
prefent Plans have each of them one; as AB hasC; and AD, the other
Side; would have another, if our Paper were broad enough: E F gives G,
and IH gives K. As to the little Squares 1, 2, 3, 4, they are the Plans
of the!Feet of the fame Chairs, and may be made broader and narrower
at Pleafure. “

Proceed then to ereét Perpendiculars from all the Angles of the Plan,
and on the Side add a Line of Elevation, MN, whereon to lay the Di-
menfions of the crofs Pieces; as O, for the lower Bars ; P for the Bars
of the Seat; and Q, for the Backs of the Chairs. Things thus difpofed,
from the Anglesof the Plan draw Parallels to the Bafe Line, as faras the
Line of Elevation, and in the Points of Interfection ere& Perpendiculars :
Thefe will give the Dimenfions, as already obferved of the former Figures.

Allthe Lines, of the Sides are to be drawn to the accidental Point of the
Plan: Thus, in the middle Chair, all the Sides are drawn to the Point G,
which is the Point of the Plan: As appears from the Figure.

102

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PRACTICAL

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ST TS SP SA RT ET 5 CTL OO PITA SOE PT

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103 PERSPECTIVE

MovEABLES laid or tumbled on the Ground.

ROM the fame Plan of Chairs ftanding on their Feet, it is eafy to
form thefé, which are laid on the Ground. * :

From .the feveral Angles of the Plan erect Perpendiculars, and give
the Side on the Ground the fame Dimenfions as that bore up above it.
- For Example, “having erected. Perpendiculars from the Angles, you'll
have the Breadth M in the Chair laid on its Side, which is drawn to
the Point K: This Meafure M, being doubled, gives O for the Bar at
the Bottom of the Chair; and the Perpendiculars raifed from the Plan,
give the Bar of the Seat P: From which Points, Lines drawn to K, will
cut the other Perpendiculars of the Front in the Places required to fhew
the {ame Bars on all the Sides they are vifible on. As to the Height of
the Back. of the Chair, make it the fame with the Height of the Seat;
but for the Back of that in the Middle, you are to draw a double Dia-
gonal, and obferve where it cuts the Rays, or Sides, RS. The reft is
obvious, | ?

The two other Figures underneath, with their Feet aloft, are eafily
performed: One of them is drawn to the Point of Sight T, the other to
the Point of Diftance VX. The Line of Elevation is Y Z.

The Method of raifing them is. the fame as for thofe upon their Feet:
That is, Perpendiculars muft be raifed from the Angles of the Plan ; and
from the fame Angles, Lines be drawn to the Line of Elevation: By which
you will obtain the Dimenfions of each of the upright Parts, and the
Places of the crofs Parts both of Top and Bottom.

103

PRACTICAL

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104 PERSPECTIVE

RELIROSPSETEE EELS ESEECR EES SEES FE So
EE SIECEN EO CONC OL COE COSC MCO LCS
(pp CHD aE LY bs CP ato ed Pia is Ig

LESECLET LESS TS SES PLaS SSSSS SSL SSS Se sos Ss

ALTARS in Per/peciive.

HE Method for Altars is the fame as for Frames of long Tables. All there is farther in the for-
mer is the Circle in the Middle, the Edges of the Cloth and the Laces: Of each whereof in its
Place.

Firft for the 4/zar, here viewed in Front, there is but little Difficulty ; for having adjufted its Height
and Length, there remains nothing but to draw Lines from all the Points on the Bafe Line to the Point
of Sight E; and from the Interfections thofe Lines make with the Bottom of the Altar, erect Perpendi-

‘culars. As to the Circle inthe Middle it is ftruck with Compaffes: The reft is obvious.

For a Side Altar fet the intended Breadth and Height in the Place where you would have it begin ; as
the Breadth AB, andthe Height B D in the Figure. Then, from B, D, and C, draw Linesto the Point
of Sight E: and fince BF is the Length of the Front Altar, and we would make this equal thereto, from
the Point F, draw a Line to the Point of DiftanceG,.and obferve where it interfeéts the Ray BC ; and
from the Point of Interfeftion raife a little Perpendicular to touch the Ray D in the Point H. Then
drawing a little Parallel from H, it will give the Point I in the Ray C3; and by fuch Means you will
have the Top of the Altar, CD HI. For the two Ornaments that are.on each Side the Circle, they
are found on the Ray B E, by drawing Lines thence to the Point of DiftanceG. M « gives the Breadth
of the Border of the Altar Cloth. Now taking the Meafure BM, fet it off from D to O, for the,
Breadth of the Cloth at the Top. As tothe Circle, we need not repeat what has been already faid of
the Method of putting it in Perfpective. We fhall only here obferve, that Lines muft be drawn from
all the Divifions thereof to the Point of Diftance G ; and in the Interfections with the Ray B, Perpen-
diculars to be raifed. ‘Then, the fame Dimenfions to be taken and fet off between B and O; as PP P.
And from all thofe Points Lines to be drawn to the Point of Sight E; obferving where they cut the
occult: Perpendiculars, and connecting the Points with a crooked Line, which gives the Circle in Per-
fpeftive. The Method of diminithing would be the fame, if in Lieu of Laces and a Circle there were
an Embroidery.

In the Figure underneath the fame Altar is fhewn free of Lines, and Points, and farther adorned with
a Crucifix and two Candlefticks. In order to this, the Corner Line of the Altar, QR, muft be pro-
longed. ‘Then, fromthe Point of DiftanceG, a Line to be drawn thro’ the Corner of the Altar T, and
continued till it cut QR; andthe Line Q R will be the Length of the Altar, equal to B Fin the firft
Figure. Hereon muft the Dimenfions of the Crofs and the Candlefticks be laid; e¢. gr. V for the Crofs
and $S, €sc. for the Candlefticks. © From all the Points S and V, Lines tobe then drawn to the Point
of Diftance G, and through their Interfe&tions with the Ray QE, little Parallels to be drawn ; which
cutting the Ray S E, give Squares upon the Altar, X X, €¥c. for the Crucifix, and Candlefticks. This
Square muft be left for the Foot of the Crucifix ; and from the Middle of the Square, the Crucifix is to
be raifed. For the Proportions of the Arms of the Crucifix, ere€t occult Perperdiculars from the Angles
of the Square, as here Y Y ; and draw Lines to the Point of Sight E, for the Candlefticks. Then turn
the Squares, for their Feet, into Circles, and obferve where they interfe& the Diagonal : For Perpendi-
culars erected from the Points of Interfection, give the Breadth of the Bafons or Stands; and Lines drawn
to the Point of Sight, the Height. Laftly, from the Middle of the }Foot erect a Perpendicular for the
Body of the Candleftick, and the Taper therein, which is to be made high or low at Pleafure. To
proportion them, draw a Line from the Top of the firft to the Point of Sight E. The reft as already

faid, ‘The Figure will call to mind the Methods.

PRACTICAL

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105 PERSPECTIVE

KAddaahershheeebaeanneddaheddhhtedisad eda tadaaedtd
JERI IOI TRIE TES.
Lo NIE DA % VIE RIS VIS RIS

WE ENY 3% I% VASA WASP IA 4 WZ pe WZ Ww WLI VA 4 S44 SAW SNA W% Wi YAN4 SA
SCOSS CSG SNE B SULIT SERS DEAS ROSS SDESAST ETSI

OE

SHOPS Zs Perfpedtive.

T R ADESMENS Shopsare ufually encompafied with Shelves, Boxes, or
Drawers, wherein their Goods are difpofed. ; oy Ma

The Rule for defigning Boxes, or Shelves, is much the fame as that already
laid down for Doors, and Windows; ¢. gr. in Lieu of the Thicknefsof the Wall
ufed in making a Window, you are here to put the Board AB, and from the
Point B, to drawa Line to the Point of Sight, C. “Then, for the Bottoms of
the Boxes; having laid down the Diftances, or Proportions of the Boards, &¥c.
in E, F, G, from thefe Points draw Lines to the Points of Diftance D. Thefe
make Interfeétions, H, 1, K, with the Ray B: From which Interfections, Per-
pendiculars are to be raifed.

For the crofs Boards, fet any Number thereof at Pleafure, on AB, or only
onthe firft Perpendicular BO; fuch are, here, L, M, N,O: From all which
draw Lines to the Point of Sight C, and their InterfeCtions with the Perpendi-
culars, in the Points P, P, €?c. give the Boxes. So that nothing remains but to
draw little Parallels to the Bafe Line ; which give the Corner of the.Box, fepa-
rating the Side from the Top and Bottom.

As to the Front Bowes, there only needs to draw Rays from the Points or Mea-
fures, and in their Interfeétions with the Line QS, to erect Perpendiculars R and
S.. The crofs Pieces are had, by drawing Parallels from all the Divifions on the
Perpendicular K; asare, here, Px, P2, P 3, P 4.

As to the Boxes on the oppofite Side, where there are fquare ‘upright Pofts to
fuftain the Shelves, their Width is had by drawing Lines from the Meafures TG
to the Point of SightC. And to get their Plan, or Square, Lines are to be
drawn from the Meafures AEF to the Point of Diftance V, which give the In-
terfections X YQ on the Ray TC. Through thefe Interfections, little Paral-
lels muft be drawn till they cur the Ray TG in Z; and from the Angles of thefe
little Squares Perpendiculars are to be erected, which give the upright Pofts, as
in the Figure. e

The Figure underneath. fhews a Shop quite fitted up, and ready to receive
Goods of any Sort: For a Bookfeller, it muft be ftocked with Books; foran
Apothecary, with Drawers and Gallipots; for a Draper, with Pieces of Cloth,

Stuff, &c. 4

FRAC TACA'L,

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106 PERSPECTIVE
kop GSP ISAS ISIS ES SFIS OH LIS ISOS NOLS LOOSEN CON INLOOLON OO SR
BuILDINGs view d onthe Outfide.

A VING now confidered every Thing relating to the Infides of Buildings,

"A. Churches, Houfes, &%c. we proceed to give Rules for the Ourfides.
Many of the Methods already laid down for the Infides may likewife ferve
for the Outfides: Thus the Method for Doors and Windows in any Part of a

Wall is itfelf fufficient for the Outfides of all Kinds of Buildings ; inafmuch as

the moft of what appears of the Outfide of a Building is Doors and Windows.
In Cafe it be enrich’d with Orders of Columns, &c. thofe, too, we have taught
to manage,

If there be Windows in Front, as A, and’tis defired to have others in the
fame Proportions on another Side, the Proportions AA A mutt be transfer’d to
the Bafe Line, as here to BBB, and Lines be drawn thence to the Point of Dif-
tance C: And in the Points FFF, where they interfect the Ray DE, Perpen-
diculars to be raifed for the Uprights in the Window.

For the cro/s Pieces ; thofein the Front Window muft be continued to the Per-
pendicular D, by which Means you will have the Points II; from which Lines
are to be drawn to the Point of Sight E, which cutting the Perpendiculars F,
give the crofs Bars in the Side-window.

If the Number of Windows were much greater nothing farther would be
required but to continue their Rays, in order to make the Meafure and Height
of the crofs Pieces the fame in all. An Inftance of which we have in the Houfe
on the other Side, which has two Windows from the fame Rays. As to the
Breadth, or Thicknefs of the Pofts and crofs Bars of Windows in Front, it muft
be fet on one of the Travers, as here on KH; and from the Corner of the
Window K, a Line be drawn:to the Point of Sight E; and from the Point H,
another to the Point of Diftance C, for the Window A, and to the Point of Dif-
tance L, for the Window on the other Side; and in’ the Point, where thofe two
laft Lines interfect, a Perpendicular, HM, muft be raifed. . Then, from all the
Corners of the Window Lines to be drawn to the Point of Sight, and from
the Points QQ, Gc. where they interfect the Perpendicular HM, Parallels
muft be drawn to give the Thicknefies of the crofs Bars. The Thicknefs of the
middle Poft, N, will be had by drawing a Line from the Corner, N, tothe Point
of Sight; and in the Points QQ, where it cuts the Thickneffes of the crofs
Bars, erecting Perpendiculars QR, QR. 7

To fix the Thicknefs of the Windows on the other Side, it muft be fet in the
Corner of the Wall, on the Perpendicular D, as the Diftance IO; and from
the Points OO, €c. Lines muft be drawn to the Pointof Sight E. Laftly, lit-
tle Parallels to be drawn from all the Corners of the Windows, asS, T 3; which,
interfeéting the Ray-O, give the:Thicknefs in the Point S. Thefe Rules may
ferve for all Kinds of Windows, both high and_low.

In the Figure underneath is fhewn a Door diminifhed according to the Rules
delivered heretofore. As, in Effeét, every Thing belonging thereto is very eafily
underftood, and readily practis’d, on fome or other of the preceding Methods.

4

PRACTICAL

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107 PERSPECTIVE

HLLALAGISELOLEL EIS OLIGLE SLE RES ES Bt)

TRAGIC ATX KG KID KI II GR GAB EA 4 SIZ CIS COIS COTS RES TUS ES,

Roors of Houfes in Perfpettive.

O O FS are made of different Heights according to their Materials. Thofe of S/aze are the moft
upright of all. Their ufual Meafure is an equilateral Triangle ; 7. ¢. their Slope, or the Declivity
of the Roof, is equal to the Width of the Houfe. Thus, in the little Figure at the Bottom of the pre-
fent Plate, C A, or C B, is equal to A B. Others make the Breadth A B equal to the Punchion, or middle
Top, DC, which is higher. But that Praétice is much lefs ufual than the former. For flat Tiles, we
only make the Roof two thirds of the Height of thofe of Slate, or of the Width of the Houle ; as in
AEB: For Thatch, the Height is ufually but half the Width: And for Pan-tiles, only one third ; as
AogB.
Before we go any farther it is to be obferv’d, that what we call Punchion, or middle Top, is a Tim-
ber rais’d perpendicularly on the Beams that fuftain the Ridge, and wherein the Raftersare all jointed.
Rafters arethe Pieces of Wood which form the Declivity of the Roof, as H I. The other Pieces in
the Corners, which goto the middle Top, are called Stays, and are ufually longer than Rafters,
asH K. 5 ‘

There are three Kinds of Roofs in ufe ; Pavilions, Pinnacles, and Pent-houfe-form. The firft have
four Sides, the fecond only two, and the laft but one.

To put a Pavilion, or Turret, in Perfpective, the Place of the middle Top muft be known, that the
Stays may be drawn tothe fame. For this reafon it was that I made the geometrical Plan LL MN O3
to fhew, that a Square, L M NP, is to be made of the Breadth of the Houfe LN, and two Diagonals
drawn through the fame, interfeCting inQ, Some put the Punchion in Q, but that advances it too far,.
and renders the Declivity of the End too {quat. It has a much better Grace when moreupright. With
this View, it fhould be approach’d towards the Wall L N a third part of the Diftance Q R, which will
bring it'to the Point S; from which Point a Perpendicular, S, muft be drawn upon the Line N P..
Then, the Meafures LT and T M to befet on the Bafe-Lines, and Lines drawn from them to the
Point of Diftance, whichis here more remote than ufual ; and from the Points, wherein they interfect
the Ray V, Perpendiculars to be ereéted to the Top of the Wall, which will give the Points XX ; from
which, Parallels to the Bafe-line are to be drawn as far as the other Ray I. Then, from the Middle of
the Wall Y, a Line to be drawn to the Point of Sight, cutting the Parallels inthe Points Z, Z, Gc. from.
which Points the Punchions are to be rais’d. To give them the proper Height regard. muft be had to
the Materials intended for the Covering, and the Height be adjufted thereby, according to the Propor-
tions already fix’d. Thus, fuppofethe Covering, Slate, an equilateral Triangle, 1, 2, 3, muft be made of
the Breadth of the Wall; and from 3, a Line be drawn to the Point of Sight, cutting the Punchions in
the Point 4. To which Point, Lines being drawn from the Corners of the Houfe, will give the Form.
of the Pavilion. .

For Pinnacle Roofs there need not fo much ado. You are only to make an equilateral Triangle, 5, 6,7,
of the Breadth of the Wall 5, 6, and the like for the. other End of the Wall, which will give you the:
Point 8. Then joining 7 and 8, you will have the Form and Meafure of the Roof.

The Figures on the other Side thew the fame Thing unembarrafs’d with Lines. The Proje€ture Rand-
ing beyond the Roof is made at Difcretion.

The Front-houfe is cover’d with a Pavilion, perform’d after the fame manner as that on the Side.

In the prefent Figure, where the Letters are, the Horizon is placed very high, to fhew the Tops
of the Houfes, and render the Practice more eafy, and conceivable. But, as it is not often fach a Cate
happens, I have added the other Figure at the Top, wherein the Horizon is as low as ufual: Tho’ the.
Rule in itfelf is the fame as that already deliver’d. a

107

TRAC TICA TL.

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a ee eee Hm en me ew wm we eee ee He
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wh tl Seg RAO arta PE EGE IE OY Pte IO EPA:

108 PERSPECTIVE

BEEBE BGG 2S BEG 1S 2G NG G2 2G 2 30 30 16 16 1 2 10 10 202016
SSA ore OP ee 8a IL PATIO ORO OR NO OCH
ESSEC CESS TELE SCE CETTE LTTE TS Ve

Sequel of the Roofs, 7# Per/pecTive.

ee
®

N the preceding Figure the Pinnacle Roofs are viewed in Front, and their

Height, where covered with Slate, fixed to that of an equilateral Tri-
angle. Where the Covering is Thatch, or Tiles, the Heights are laid
down on the Figure underneath.

Now, to make thefe latter Roofs with Returns, the Width of the Bot-
tom of the Houfe muft be fet on the Bafe Line, as here AB; andof this
Width a Triangle is to be formed with the other Dimenfions, according
tothe Form of the Roof. The prefent is an equilateral Triangle, where-
of CD isthe Height intended to be fet perpendicularly on the Corner of
the Houfe, at the Height of the Wall, as here EF. Then the Breadth
of the Houfe is to be laid down in C, which is the Middle of AB; and
from thence a Line to be drawn to the Point of Diftance; and in the
Point G, where it interfeéts the Ray A, a Perpendicular mutt be raifed,
Laftly, from F, a Line to be drawn to the Point of Sight X ; the Inter-
feCtion whereof with the Perpendicular H, will be the Point, or Tip of
the Pinnacle; to which Lines muft be drawn from the Corners of the
Houfe, EI. If you would have Eaves, they are eafily ‘added: As is feen
in the Figure on the other Side, D, :

For Pentices, you have only to draw a Line for the Height of the
Roof, as here the Line LM, and give it any Declivity at Pleafure. In
the prefent, the Height of the Roof MN, is the fame with the Breadth
of the Building, NO. If then, from the Points MO, Lines be drawn
to the Point of Sight X, the Perpendicular of the Depth will be cut in
the Points P and Q; which being conneéted by a right Line will form
the Koof. The Figures on the oppofite Side fhew Houfes covered after
fuch Manners.

Thote a Top are only intended to thew that the fame Rule is to be
obferved, tho’ the Horizons be changed, ;

A Church is feen in the Middle, which is covered or roofed with Pi-
nacles ; and the Wings with Pentices.

There is alfo a Pavilion viewed end-wife; mention whereof has been
made in the preceding Page. 4

108

PRACTICAL

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109 PERSPECTIVE

CDE ADE DESIST HGR EGE ESSN Gages) 79
CES GeISICHSICEYSIES SY Ce SIRS SICHSI ESS

sk Be
To put a Street in Perfpective.

en Sight of the Figure muft fuftice to fhew
the Method, which is exceeding eafy. All
you have to do is to make a Plan of fimple
Squares, the common way 5 and to take one, or
two, or three of the Squares for the Breadth or
Length of each Houfe; and on fuch Breadth,
€Pc. to fet off the Meafures of the Doors, and
Windows; and to get the Dimmutions by draw-
ing Lines from the feveral Meatures to the Point
of Diftance ; as here from BC DE and F.

The firft Angle of each Houfe may ferve for a
Line of Elevation, as the Angle G in the firft
Houfe. As to the Roofs, we have already faid
how they are to be manag’d. |

If you require any crofs Streets, one, two, or
three Squares are to be left vacant, and nothing
upon them, as are here H andI.

The Figure underneath is to fhew, that. where
Houfes are to be made advance, or fall back, you
have only to put their Elevations forwarder or
backwarder on the Plan of Squares. Thus L ad-
vances a Square farther than K, and M farther
than L; and fo of the reft. ae

109

PRACTICA &

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1i6 PERSPECTIVE
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Peecersepereanveerrtrrrerverirrertr irr itr er ricer

That remote Objeéts do not foew
their Ihicknefs.

T muft be here remember’d, that Objects near
the Horizon, that is, fuch as are extremely re-
mote, are not to fhew any Thicknefs when view’d
in Front. ‘Thus, for Example, the Houfes A, B, .
C, D, fhould not have any Thicknefles of the
Windows, Doors, &c. but only mere Lines. The
Reafon is, that the vifual Rays proceeding from
the front Parts of the Object become united in
the Eye with the collateral ones.

I fhould have given a ftrict Demonftration
hereof, had I apprehended it any way neceflary.
But as I don’t fee of what ufe it would be, and
as I ftand engag’d from the Beginning of the
Book not to enter into fuch Demonftrations, by
reafon I fuppofe I have to do with People who are
but indifferently prepar’d to underftand them, |
decline it.

PRACTICAL. 110

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PERSPECTIVE

NAD ENENENENENEN
RONG

GAQDE

BuILDINGS viewed by the Angle. ©

7 F thefe two Building feen Angle-wife the firft is performed after the Man-
O ner already delivered for Squares viewed the fame Way, and Elevations of
other Things in Side-views. However, to fave the Trouble of recurring to the
one andthe other, we fhall here obferve, that to perform fuch Buildings the
Meafures muft be fet on the Bafe Line, and from each of them, Lines be drawn
to the Point of Diftance, and from the Points of Interfection Perpendiculars
to be raifed: The firft Angle ferving fora Line of Elevation, ‘Thus, in the
prefent Building, the Breadth being AB, and the Length, BC, double its
Breadth ; from A and B, Lines are to be drawn to the Point of DiftanceD,
and from B and C to the Point of Diftance E; and from the Interfections BF
and G, Perpendiculars to be raifed for the Corners of the Houfe. As to the
Dimenfions of the Doors and Windows, they muft be laid down on the Bafe
Line between A B and BC; and Lines be drawn from them all, to the Points of
Diftance Dand E. Then, obferving where BDor BE are interfected thereby,
raife the Pofts of the Windows therein. The Perpendicular of the firft Angle B
ferving for a Line of Elevation, will give the crofs Pieces, and the Height of
the Windows. The reft is obvious.

As to the Figure underneath; the Method is the fame as for Chairs placed ir-
regularly ; i.e. having made the Plan, put it in Perfpective as irregular Objects
are put: Then, laying a Ruler along each Sideof the Plan, obferve where it cuts
the Horizon, and marking the Point, draw Lines thereto from each Part of that
Side of the Building. Every Side or Face of a Building has its particular
Point. Thus the Plan being put in Perfpective, the Side, HI, gives the Point
K on the Horizon, to which all the Rays on that Side muft be drawn. The
other Side, IL, fhould likewife have its Point; but for want of Paper-room,
we could not here exprefs it. Thefe two Points found, a Ruler muft be laid
thereon, and an occult Line drawn over the other Side of the Building parallel
upon the Plan to that which gave the Point in the Horizon, and continued to the
Bafe Line ; as from R/fthrough L to M; and from the other Point continue an
occult Line through Hto N. Then fetting the Number of Windows of the
Side HI, between N andI; and between I and M, fetting the Number of Win-
dows on the Side IL, draw Lines from all thefe Points, or Meafures on the Bafe
Line to the Points in the Horizon: And proceed as in the Figure above.

4

PRACTICAL EID
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112 “PERSPECTIVE

EP Ose 8 x OOD 3p COB x. 30 COM v0 x OB ye x EOP
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To put Walks, with Rows of Trees, in Per-
Jpettive.

HO’ the preceding Rules might furnifh fufficient Inftruétions for putting
Walks with Trees in Perfpective ; we have judged it not amifs to add a par-
ticular Rule which may render the Method ftill more eafy.

if only a fingle Row of ‘Trees on each Side be required, there is no need for
making a Plan of Squares, or Checquers: What is directed in Pag. 17. will
fuffice. |

But where a Number of Walks are to be fhewn, we think it advifeable to form
a Plan in occult Icines, with Trees, as already taught in Pag. 31. and from the
Diagonals of the little Squares formed thereby, to erect Perpendiculars, as is
fhewn in AB. If you defire to have the Trees farther or lefs apart, increafe or
diminifh the Diftances of the Squares on the Bafe Line.

When you have given the Stem of the firft Tree its proper Height, as AC,
draw a Line from C tothe Point of Sight D, which Ray CD is to bound the
Stems of all the other Trees. The firft Tree, A'B, fhews that you may give
them what Turn or Form you pleafe between the two right Lines; and that they
are not tobe drawn with the Straightnefs of a Ruler. 3

The Figure underneath is performed as that above, all the Difference is, ¢hat the
Squares of the upper are direét, or in Front; and thofeof the under, viewed
Angle-wife: Whence the Meafures on the Bafe Line, in the latter Cafe,’ muft be
all drawn to the Points of Diftance E and F ; Perpendiculars to be raifed from
the little Squares, and the reft as above.

In the fame Perfpective, wherein are Walks drawn to the Points of Diftance,
one may add others, drawn to the Points of Sight. Thus the middle Walk tends
to the Point G, which is the Point of Sight; and the others to the Points E, F,
which are thofe of Diftance.

———7E soos

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PRACTICAL

E13 PERSPECTIVE

Si, x CORD x. x SOT x, COM x Bp Ke CORD a CRA ox BORD, x He
CS CREO GERD GOSO ™ ee * GORD * WOO ™ “GSGO™ BS
| CSOKEWOSOKERODOERISS ENISHI NOCIOM BISON

To put Gardens in Perfpective.

N the Doétrine of Plans has already been fhewn the Manner of diminifhing,

or putting the Plan of a Garden in Perfpeétive, by an eafy Rule; fuppofing
that you have the Plan thereof. But, as I always endeavour to avoid geometrical
Plans, by Reafon it takes up too much Time to make them, I have added the
prefent Figures: Whereby it appears, that having made a Checquer, or Plan of
Squares, you may take as many or as few of them as you pleafe for the Beds of the
Garden: As here, A and B have each of them three Squares every Way ; the reft
ferving for Walks, as CC. If you would have Compartments, or Knots in the
Beds, you are to ufe the little Squares or Divifions of each Bed 5 cutting them,
and forming of them the Figure required ; as is fhewn in the Squares of AandB;
and thofe of the other Side, Dand E. The Pallifades and Arbours are cut thro?
the Breadth of the Walks.

Be hatch kc k aese sheets afte otststssestsk ab fe esheets dio Bl Poh

Beds with Borders.

W HEN Borders are to be given the Beds, the intended Heights and Breadths
muft be fet on the Corner ; and from thofe Meafures, Lines be drawn to
the Point of Sight. Thus, in the lower Figure, FG being the Breadth and
Depth of the Borders of the Bed H, Lines muft be drawn from the Angles of
the little Square F andG to the Point of Sight I; and go on with the reft, as
_abovefaid.

For Arbours, upright Pofts, or Perpendiculars, OO, &c. muft be raifed from
the Angles of the Squares of the Walk. The reft as already direéted for Arches
viewed Side-wife, in Pag. 60.

The Grove in the Middle is performed by erecting Perpendiculars from all the
Angles of a Checquer, &e. |

A

PRACTICAL 113 ‘

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BEDOK SBODOKEHODOKEW KE RODS RNIODOSM IE
To put Fortifications 7m Perfpective.
W E need not here repeat the Method of di-

- minifhing, or putting in Perfpective, the
Plans of all Sorts of Fortifications :. What has al-
ready been faid in Pag. 39. is clear enough.

To raife them there is no more Difficulty than
in a bare Wall; only more Time is required, by
Reafon of the greater Number of Angles which
are to be drawn all to the Line of Elevation, to
cive their Heights thereon ; as has been mention’d
over and over in treating of other Works.

The little Line of Elevation is divided into
four Parts: The firft, from 1 to2, 1s the Height
of the Parapet of the covered Way; from 2 to 3,
is the Height of the Rampart; from 3 to 4, the
Height of the Parapet of the Rampart ; and from
5 to1, the Depth of the Ditch.

114.

PRA C31LE Af,

6

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115 PERSPECTIVE

PSRPRSSHLPPSSLELLES LEP LEERESRER DEG S&S ew
CESS LOOMED) CO MOON LOD COE
RI Fs PIs (PI (Gd BAYS LIP oP Ly a PF

SLES CLS SL SES SSSSS SS FSS SPSS SESE TE SSO SSS

To make Defigns in Perfpective.

HERE isno Mafter fo excellent, but makes Defigns of the Works he
would fucceed in. If this be ufual in moft Arts, *tis neceffary in this, by
Reafon of the great Number of Points, and Lines to be ftriétly obferved, and
nicely managed, without which nothing is to be done in any wife pleafing to a
Perfon that has any Tafte or Skill therein. vi
Since then there isa Neceffitry of making Defigns, weare to look out for what
may be affiftant therein. And as every Body knows that the Length and Te-
dioufnefs of fuch Works lyes in the drawing of Parallels and Perpendiculars, f
have fought both in Authors, and in Experience, for a Method of doing the
fame as expeditioufly as poffible. The Refult is, that nothing of this Kind has
appeared to me worth the recommending, but the Plate and Square, which Viator
has left us in his Writings; which are Things fuch People, as have Occafion to
fpend much Time in defigning, will find a deal of Eafe and Benefit from.

Tho’ the Figure gives a tolerable Notion of the Thing, and the Method of ufing
it, it may be convenient to give fomething more exprefs thereon. The Plan AB
€D, then, is to be perfectly on the Square, a Foot and ahaif long, fifteen Inches
broad, and half an Inch thick. The Wood to be dry, firm, and fmooth. To
make it the fofter, and favour the Pen, a Sheet of Paper may be ftuck on it.
The Square EF is a Ruler a Foot and a half long, an Inch broad, and a Quar-
ter of an Inch thick, fitted at right Angles in another Ruler, GH, eight Inches
Jong, one broad, and three uarters of an Inch thick. Now to draw Lines,
this laft Ruler, GH, is held clofe to the Board ABCD, in which Cafe the
vei Ruler, EF, is certainly right, provided the Board and Ruler be exactly
ormed. _— \

When you go to Work, faften the Sheet of Paper, IK LM, o@ the Board
with four little Pieces of Wax, NOPQ; then may you draw Lines\ from any
Point, fecure that they are right. -And-for Perpendiculars, you have only to lay
the Handle, or Crofs of the Ruler, GH, on the Side GD, in which\Cafe EF
will be perpendicular to C D. mote | V\ |

For myfelf, I finda” wonderful Eafe herefrom. The~Fruth ts, withqut fuch
a Contrivance;a Man muft never be without the Compaffes inmhis Hand. All
the Trouble now remaining is for the vifual Rays. And for thefe, fome ufe a
Ruler perforated at-one End, and faftened by a Needle to the Point of Sight.
But this is to’ run into a Trouble greater than what you would avoid, The com-
mon Ruler does every whit as well.

R is a common Ruler. ~~

T a Pair of common Compaffes.

V Another Pair of Compaffes, with a drawing Pen therein’; for circular Lines,

Thefe are all the Inftruments neceflary for making of Defigns in Perfpective.

a ES EE NR

PRACTICA E£,

Sin, OE WR AS RE A EN AE I NESS LET

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116 PEARS PE QT rv:

PLE SLE RRR SSO BLS LSI NN oe

Reduétion of Perfpettive Draughts out of Small into Great; and out of
Great into Small.

S Defigns are made with more Eafe in little than in great, ’tis but reafonable they fhould always
A befomade. This has put me on givinga Method of enlarging fmall Defigns on the Canvas.

‘Lhe Method commonly ufed by. the Painters is to divide their little Defigns, and the Canvas they in-
tend the large ones to be on, into an equal Number of little Squares, and to transfer what is in the
Squares of the Defign, into the correfpondent Squares of the Canvas. This Way fome greatly approve of,

Here follows another, which, in my Opinion, is eafier and furer. Provide a Scale proportionate to
the little Defign, and another proportionate tothe Canvas. To make a Defign the firft Thing to be de-
termined is the Scale, which is to fix the Meafures of all the Parts of the Work. Thus, in the little De-
fign A, the Seale B C of five Parts, which we may call Feet, is the firft Thing made. From this Scale
are taken the Horizon, the Height and Diftance of the Trees, the Breadths of the Walks, &&c.

To enlarge this Defign the Method is this: Confider whether or no the Draught is to have its natu-
ral Horizon, 7. ¢. Whether, when the Bottom of the Painting is on the Ground, the horizontal Line be
the Height of the Eye, which is about five Foot. Then, of the five Divifions between B and C, make
a Scale of five Foot, FG, that thus, having taken all the Meafures and Proportions in the {mall one,
you may transfer them to the great one, after the following Manner.

The two Scales thus fixed, the firft Thing to be done is, to take in your Compaffes the Diftance be-
tween the Bafe Line D, and the Horizon E, and to apply the Compaffes thus opened, to the little Scale
BC, nothing what Number of Parts itincludes, as here it does five. Take therefore five Divifions on
the large Scale F G in your Compaffes, and fet them on each Side the Painting, or large Defign, begin-
ing at the Bottom of the Cloth HH, and ending inII. From the Points II, ftrike, or fcorea Line
with a chalk’d or blacken’d Packthread. This Line I I, will mark the Horizon in the large Draught.
Then take the Diftance, or Depth, K L, of the little Defign, which gives the Foot of the Houfe, and
fet it on the little Scale: Note how many Divifions it includes, and take the fame Number from the
large Scale, and fet them on the Edges of the Canvas, HM, HM, which you muft ftrike with a Pack-
thread, for the Depth of the fecond Tree. Proceed.to take in the little Defign, the Diftance NO, and
fet it on the little Scale, then take as many inthe large one. Again, NO includes two Parts of the little
Scale; accordingly two Parts are to be taken on the great one, and fet off from H to P, which mutt be
ftruck as:before. Do the fame for all the Parallels to the Bafe Line, as the other Trees, Windows,
Roofs, Se.

As to Perpendiculars to the Bafe Line the Method is the fame as for Parallels; only that they are to
be ftruck or fcored not from the Side, but from the Top and Bottom. Thus, for the two Corners of
the Houfe, the Interval between them being taken in the Compaffes, muft-be {et on the little Scale, and
being there found equivalent to feven Divifions and a half, as many Divifions muft be taken from the
great Scale, by which you will have HS T'S, to be ftruck as before. And the like mutt be repeated for
all the other Perpendiculars, as Buildings, Trees, Pallifades, &'c.-._

To find the vifual Rays, which are the Lines proceeding to the Point: of Sight V, faftena Pack-
thread to this Point V, of the Length of the Painting, and with this ftrike of {core all the Rays very
exactly. Thus, forthe two Rays D X, which give the Breadth of the Trees in the little Defign, take
the Diftance D X, fet it on the little Scale BC, and take an equal Number of Divifions from off the
great Scale, this will give you H Ys to which Points Hand Y, ‘Lines are to be ftruck with the Pack.
thread, fromthe Point V. For the Ray of the Pallifades, take the Diftance D Z, and fet it on the
little Scale, and take as many Divifions from the large Scale ; by this Means you will have H +, which
are to be ftruck from the Point V, as before.

Every ‘Thing in a Perfpective ordinarily comes under one or other of thefe three Sorts of Lines, Paral-
lels, Perpendiculars, and vifual Rays: And having fhewn how to defcribe thefe with a good deal of Eafe
on the Canvas, there remains nothing formidable in the reducing {mall Defigns into great.

As tothe reducing great into little, you have only to invert the Procefs; that is, take the Meafures
firft on the large Scale, and diminifh them proportionably on the fmall one. Thus, if the Horizon of
the large Defign were five Divificns of the large Scale, five Divifions of the fmall Scale were to be ta-
ken for the Height of the Horizon of the {mall Defign. And fo of the reft.

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PRA CTICALE

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117 PERSPECTIVE
HosRELESOTS THES TR TSR Tae Sa eS

Apparatus fo the univerfal Method of the Sieur G. D. L.

A S many of the People, for whofe Benefit I.intend this Work, may not be deep enough to fee clear-
ly into this univerfat Method, the Author, I believe, will allow’me to make it as eafy as I can,
that they may be the better enabled to reap the Benefit thereof. ’Tis for this Reafon I have added the
two following Figures, which will call to mind what has been already touched upon in the fecond, third,
fourth and fifth Advertifements. The Defign whereof was to facilitate this Method, and accordingly
in them is fhewn how to take all the Meafures on the Bafe Line; and thatas many Rays as cut the Dia-
gonal C F, fo many Squares are formed in the Depth of the Draught ; which Squares may be made of
any Magnitude at: Pleafure.

Now, not to have fo far to feek, view the firft F igure, where the Bafe Line is A B, the Point of Sight
G, and the Points of Diftance EF. This Bafe Line I divide into twelve equal Parts, which I fuppofe
equivalent each to one Foot, and from all the Divifions draw Lines, or Rays, to the Point of Sight,
whereof A and B are the laft. Now, ifa, Line fhould be required that is funk a Foot deep inthe Draught,
draw a Line from the firft Divifion, B D, to the Point of Diftance F; and where this Line D F cuts the
Ray BG, will be the Point for a Line to be drawn through, that is funk a Foot. If another, two Foot
deep, were required ; take three of thefe Parts on the Bafe Line, and from the third dfaw a Line to the
Point of Diftance F, and the Point where it interfeétsB G, will be the Place for that Line. Confe-
quently, if from C.a Line be drawn to F, the Point where CF cuts BG will bea Line fix Foot deep.

If of the other fix Parts remaining of AC, you make twenty four, by dividing each into four, and
yet account each Divifion a Foot, you will have twenty four Feet between A and C; fo that if a Line
thould be required eighteen Foot deep in the Draught ; I would reckon eighteen little Parts from A,
and from the eighteenth would draw a Line to the Point of Diftance E, which by its Interfection with
AG would give one Point for that Line. If a Line were required twenty four Foot deep, the whole
Line A C mutt be taken, and from C a Line be drawn toE, and from H, the Point wherein CE cuts
AG, the Line HI muft be drawn, to appear twenty four Foot deep in the Draught. :

In Perfpective, the Line H I is equal to that of AC, i. ¢. contains as many Parts, or Feet. So that
if from Ia Line be drawn to E, the Interfeétion of I E with AG, will give the Line K L forty eight
Foot deep. And if from the Point L, a Line be drawn to the Point of Diftance F, by its Interfection
with the Ray A G, you will have a Line twenty four Foot farther off than the other.

If you would have a Linethirty Foot deep, from the Point A reckon fix fmall Divifions, and from
the fixth draw a Line to the Point of Sight G, obferving where it cuts the Line HI, as here in the Point
M. Then from M draw a Line to the Point of Diftance E, and the Line ME will interfe@t the Ray
A G in the Point N, through which the Line required muft be drawn, If a Depth of forty. Foot were
required, from A fixteen Divifions were to be reckoned, and the reft, to bedone, as before. If fixty
Foot be required, twelve Divifions muft be taken, and from the twelfth a Line be drawn to the Point of
Sight G, as far as the Line K L, which will give the Point O. ‘Then, from O, a Line to be drawn
to the Point of Diftance, and its Interfe€jon with the Ray A G, will give the Line.

As to the fecond Figure, from what has been faid it is eafy to find a Point of any Depth or Diftance
at Pleafure. It remains to thew how the fame is found within er without the RaysA Gor BG. Inorder
tothis, the Line BC is toferve asa Scale of fix Foot, one of which we divide into twelwe Inches; that
we may have the half, third, fourth, (7c. of a Foot, Things thus difpofed, if it be required to thew
a Point feventeen Foot diftant, and a Foot and half within the Ray AG, a Line muft be drawn from
the feventeenth Divifion of the Bafe Line, to the Point of Diftance E, and where the Ray AG isin-
terfected thereby, in P, the Line P Q to be drawn. Now, fince a Foot and half is required within the
Ray AG, I take the Extent on the fame Line N Q in my Compafiés, and fetit off from P to R, which
Point R is the Point required. _ If a Point twenty nine Foot diftant, and feven and a half within the Ray
AG be required, a Line muft be drawn from C to the Point of Sight E, and through the Point where
it cuts AG, a Line being drawn, gives twenty four Foot. Then, from A taking five lefler Parts, a
Line muft be drawn from their Extent to the Point of Sight G, till it cut that Line inthe Point S ; and
from S a Line is to be drawn to the Point of Diitance E, and from the Point wherein iit cuts the Ray
AG, aLine, TV, muft bedrawn. And fince feven Foot and an half are required beyond the Ray A,
that Space muftbe fet on the fame Line from T, towards V to the Point X, which Point X willbe the
Point defired. After fach Manner, may any Diftance at pleafure be determined:

a

117

PRACTICAL

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An univerfal Method of performing Perfpecive without having the Point of Diftance out of the Painting, or
Ground of the Work; made publick by the Sieur G. D. L.
N this Method a geometrical Plan is required, or at leafta Scale of Meafures both for the Plan, and
I the Elevation, in order for the one or the other to be put in Perfpective.

Foran Objes or Subject, we fhall take the Author’s own Example, which is a fquare Cage, termi-
nating a Top ina Point, or a Building witha Pavilion Roof. The Meafures whereof fhall be given by a Scale.

Now having made the Plan of the Cage, mids, which is here added at the Top of the Figure, a
Line, a4, mut be drawn at the Diftance the Object is to appear at in the Draught, as here the Line, @ 4,
17 Foot, which is to be the Bafe Line, or Bottom of the Piece, and to be placed according to the Afpeét the
Obje&t is to be viewed in. Then, from the z Extremes of the Line a, 2 indefinite Lines muft be
drawn parallel to each other, as the Lineag, and bg. On1 of which Lines, as ag, you are to draw
little Parallels to the Bafe Line, proceeding as far as the Angles of the Plan, and by Means of the Scale
fee how far each Angle of the Plan is removed from this Line ag, and mark the fame on each Line. Then,
from the Place the Painting is intended tobe viewed from, which is here the Point c, 5 Foot diftant from
&, deferibe a Perpendicular to 24, viz. the Line ¢#; and to this Line allow as many little Parts of the
Scale, as the Spectator is to be diftant to view the Painting, viz. 24 Foot. At the Extreme of which 24
Foot, which is the Point ¢, ereét a little Perpendicular, of the Height of the Eye, wiz. the Linet /,
equal to 4 Foot and an half.

The Cloth, Wall or Paper thus difpofed for putting the Plan in Perfpe€tive, and making the Elevation
on the Plan, divide the Bafe Line, A B, intoas many Parts as ain the Plan is divided into, wiz. twelve,
each accounted a Foot ; and over the Points A andB, fet the Height of the Line /¢, vix. four Foot anda
half; that is, taking in your Compaffes four anda half of the Divifions of AB, fet them perpendicularly over
the Points A B, by which Means you will have the Points E and F. Draw the Line E F, therefore, parallel to
AB, and it will be the Horizon. Then, as in the Plan, the Point C, which is the Place the Draught is to be
viewed from, is five Divifions diftant from 4, you are toreckon as many Parts from B ; and from the fifth,
C, ereét a Perpendicular to AB, which cutting the Horizon in the Point C, gives the Point of Sight to
which all the Rays AG, and BG, reprefenting the Parallels of the Plan ag, and 4 g, mutt be drawn.

As to the Point of Diftance, it will be the Point F, and as the Line c#is 24 Foot long, 6 Divifions
mutt be taken from the Line A B, viz. from A to D, and each fubdivided into 4; which 24 Parts
are to ferve asa Scale for the Depths or Diftances, being fufficient for the fame, tho’ they were infinite.
And the 6 Parts remaining between B and D, will be a Scale for the Feet, according as the Lines drawn
from the Points found for the Plan, fhall cut the Rays drawn to the Point of SightG. Foras this
Scale is a Pyramid, whereof B D is the Bafe ; the Meafures diminifh in Proportion as they are farther off.
One of the Parts is divided into Inches, thac all the Meafures may be there, as onthe Plan.

By the Scale of Diftances, the Points of the Plan are found, and by the Scale of Meafures the Lengths
of the Lines both of the Plan and Elevation.

Now to put the Plan in Perfpective, all the Meafures of the geometrical Plan muft be obferved. The
firft Angle of the Planr m is 17 Foot diftant from the Point 2, onthe Line ag. For this Reafon we
reckon 17 Parts, beginning at A, and from the feventeenth draw a Line to the Point F, cutting the
Ray AGinR. From this Point, R, a Parallel to the Bafe muft be drawn: And by Reafon the Plan m
is within the Ray ag, by a Foot and an_ half, therefore, on the Side B Dof the:-Line R, muft a Divifion
and an half be taken, and fet off within the Ray A G, which will give the Point M, reprefenting the
Angle of the Plan. As tothe Angle 4, which is 26 Foot diftant from the Point a, a Line muft be
drawn from the Point D, which is 26 Foot from A, to the Point F; and where the Ray A G is inter-
feted thereby, viz. in the Point y, a Parallel is to bedrawn. Nowzas the Pointy is not remote enqugh
by z Foot, a Line muft be drawn from the fecond Divifion of the Scale to the Point G, and where this
Ray cuts the Parallel y, viz. in the Point Q, the Line Q F to be drawn, which will. give the: Point H
on the Line AG: From which Point’H a Parallel to AB-muft be drawn, and on the Side B D of the
fame Line H, mult the Divifions for 14 Foot and an half be taken, viz. from the Point H to L.

For the Point 4, which is 29 Footdiftant from A, a Line mutt be drawn from the fifth Part of the Scale
AD, tothe Point G, and where this Ray interfeéts the Parallel y, wiz. in the Point O, the Line O F muft
be drawn, which gives the Point N on the Line AG. Then from N draw a Parallel, the Side whereof,
BD, 7 Foot and a half mutt be taken, to be fet off without the-Ray AG, viz. from N to K.

For the Point i, which is 38 Foot froma, take 14 Divifions on the Scale AD, and from the four-
teenth draw a Ray tothe Point G, which cutting the Parallel in the Point S; from that Point draw a Line
to F, cutting the Ray AG in T, which is 38 Foot from the Point A, inafmuch as the Parallel y is 243
to which, 14 being added, gives the whole 38. And fince the Angle iis 4 Foot and an half within the
Ray AG, that Extent muft be fet on the Side D B of the Parallel T, wiz. from T to I.

To form the Plan, thofe four Points MLK I muft be conneéted by right Lines, and Perpendiculars
ereéted from their Angles, asM /, Lf, K fr, and Ip; each of which will be feventeen Foot, asis ex-
prefs’d inthe Plan by the Line X. Then, from the Extremes of thefe Perpendiculars, draw two Dia-
gonals /, /p, and ff, fr, which interfeCting in Z, from the fame Point Z erect a Perpendicular, Z #,
thirteen Foot and ahalf. Laftly, drawing Lines from all the four Angles 7, f, /p, and fr, to the Point
#£, the Cage will be formedin Perfpective. If you would have it funk a Foot under Ground, adda
Feot underneath each Point of the Plan, and conne& them by Lines. 2

118

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To give any precife Diftance required, without removing the Point of Sight
| out of the Prece. 2

S U CH as are difpofed tomake ufe of this univerfal Manner ought to know, that the Number of
Feet you take on the Bafe Line are to have a regard to the Point of Diftance. propofed.

To make the Propofition underftood : In the firft Figure are put two Points of Diftance, the one fix,.
the other twelve Feet; which have an eafy Ratio to each other; inafmuch as the fix Parts being each di-
vided into two, you have twelve. pas

Suppofe then the Line A B divided-into twelve Parts, and from each Divifion Lines drawn to the
Point of Sight C; take half thefe Divifions, A D, and from D to the Point E, which is the Diftance of
fix Feet, draw DE. ’Tis certain its Interfe€tion with the-Ray AC will give the Diminution of the
Squares viewed at fix Foot Diftance. Andif from Da Line be drawn to F, which is the Diftance of.
twelve Feet, the Line DF cutting the Ray AC will give the Diminution of fix Squares, view’d at a
Diftance of twelve Foot. And if the Diminution of twelve Squares, viewed at twelve Foot Diftance, ,
were required, from the Point B, which is the whole Bafe Line, a Line muft be drawn to F, and its
Ynterfeétion with the Ray A C, in the Point H, will givethe Thing required. Or fromI a Line IF is
to be drawn, which will give the fame PointH, the Line HK, in each Cafe, being the Depth of twelve
Squares, viewed at twelve Foot Diftance. Hence we obferve, that twelve Squares, viewed at twelve
_ Foot Diftance, meet in the fame Line HK with fix Squares viewed fix Foot off, and that all the Lines
of the fix Squares, given by the Interfection of the Diagonal D G, havea Relation two by two to thofe
given bythe Diagonal DF. The Reafon why the Diagonal DF givestwo Lines for one of thofe.
DG, is, that the. Diftance is double. If it were triple, ic would give three, and four if quadruple.
Now, to find the fame Interfeftions, and the fame Number of Squares on the Side B D, asare on that AD,
without having the Point of Diftance out of the Piece, you have only to divide each of the fix. equal
Parts between Band D into two, by which Means you will have twelve Parts: ‘Then draw occult.
Lines from each. Divifion to the Point of Sight C, and drawing Parallels to the Bafe Line thro’ all the
Interfections the Diagonals make with all thofe Rays, you will have twelve Squares Depth in the fame
Line as if the Diftance were twelve Foot, tho’ in Reality G be but fix. ‘The Reafonis, that in multi.
plying the Rays you multiply the Squares, and multiplying the Squares you remove the Diftance far-
ther. Suchis the Reafon why having made tweive Parts of the fix that were between B D, there are pro-
cured twelve Squares, which have the fame Depth as if at twelve Feet Diftance. And if a Diftance of
twenty four Feet were required, you have only to divide each of the Parts between B and D into two, .
which making twenty four Parts, from the twenty fourth draw a Line to the Point D, and the Point K,
wherein it interfeéts the Ray B C, will be the Depth of twenty four Feet.

In the fecond Figure the fame Meafures are laid down on the Line L M, asonABof the firft Figure, .
and thefame Depth and Diftance on the Side MN, as on the Side A.D, which-gives the Line H K ; to.
fhew, that if a Line were drawn from the fifth Part, as QG, or from the feventh, as RG, the true:
Depih would not be had, which is at K.. For RG would not fink it enough, and Q G would fink too.
much; even tho’ of thofe five or feven Parts there were made twelve or twenty four. ;

For this Reafon you are always to obferve to take a Number which may be multiplied by the Di-
ftance, as here the Diftance of 6 may ferve for 12, 18, 24, 30, 36, 42, 48, &c. the Diftance 5 may
ferve for. 10, 15, 20, 25, 30, &%c. and the Diftance 8 for 16, 24, 325 40, 48, ce. Im this Way you:
cannot fail ;- for fuppofing the Point of Diftance cannot be nearer the Point of Sight than G is to C, it
follows, that if G be fix, feven, eight, or ten Foot from C, that then half the Bafe Line will have.
the fame Number, which isto be divided proportionally to the Diftance intended. For Imftance, if there
be eight Foot from N toL, and I requirea Diftance of thirty two Feet, without moving G out of
its Place; I divide each of the eight Parts, or Halves of the Bafe Lines, as LN, into four, accordingly,
four Times eight make thirty two Rays. So that the Diminutions of the Squares will be thirty two Foot
diftant. . ;

Thefe little Divifions do none of them remain after the Painting is finifhed, only the principal Divi-
fions of Feet, which are drawn to the Point of Sight, and the Diminutions, that is, the: Parallels to the.
Bafe Line, which ftill ftand. 1

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PRACTICAL,

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Avery curious Method of drawing all Perfpectives in the moft natural Man-
3 ner, without obferving the Rules.
H AVING given youall the Rules to be obferved in drawing of Perfpec-
tives in the exaéteft Manner, I have thought fit to add this and the fol-
lowing Method of drawing the fame very elegantly and exactly, without being
tied to the Obfervation of any one Rule. ;

It may be of good Service to fuch as love Painting, and take Pleafure in prac-
tifing the fame, without being willing to beat the Pains of opening the Com-
paffes, or taking up the Ruler, to draw Lines. For in this Method neither the
one nor the other are required ; and yet thé fineft Draughts may be made here-
by, of Buildings, Gardens, Landskips, c.

Before we come to the Method itfelf, ic muft be obferved, that the principal
Requifite therein, is a large Piece of fine clear Glafs, fitted in a fine wooden
Frame, expreffed at the Bottom of the Plate by the Letter A. This Frame is
to flide between two Cheeks, or Pieces of Wood an Inch anda half thick, which
are raifed at the two Extremes of a Board the Breadth of the Frame, 7. e. about
a Foot broad, as fhewn in. BC, which is difpofed to receive the Frame A. In
the Middle of the Board one or more fquare Holes muft be made, as in E, to
receive the flit Ruler F, fo as it may be raifed or lowered at.Pleafure. At the
Top of which Ruler is a Circle of three or four Inches Diameter, but no Thick-
nefs, being made of Tin, or the like, and having a little Aperture, about the
Size of a Pea, in the Middle. The whole is reprefented together in G.

Now, tho? the mere Figure fhew the Application, yet we fhall defcribe the
Method of Proceeding. Having, therefore, placed the Inftrument G before
the Object you would draw, look thro’ the little Hole, or Sight, F,. and if you
fee all the propofed Objects reprefented on the Glafs, the Inftrument is fixed,
otherwife, bring the Sight nearer the Glafs, till you fee the whole of what is re-
quired. The Piece thus rectified, you are to draw on the Glafs every Thing that
you fee thereon thro’ the Hole F ; which hasthe fame Effect here, asthe Point
of Sight in the other Methods. And itis certain, every Thing thus drawnon the
Glafs, the Eye being fixed to the little Hole, will be according to the ftri&
Rules of Perfpedctive.

Every Body knows how to take, or copy off what is thus defign’d on the Glafs,
*Tis beft to draw the Lines and Figures on the Glafs with Pen and Ink, then
wetting the Backfide of the Glafs a little, and laying a moift Sheet of Paper on
the Side that has the Defign, rub or prefs the Paper gently thereon with the Hand,
and the whole Draught will be impreffed or transferred fram the Glafs upon the
Paper.

Some advife to make ufe of a Pencil and Colours, and in Effect, every Body
is left to their own Difcretion. ’T is enough to know the Method in general. A
Defign of a Palace is as-eafily taken this Way as ‘a Landskip,. and a Church as
a Houfe or Chamber: All required in any of them being to pitch on a Place
where the whole Thing to be reprefented maybe feen, and to bring the Sight to
the proper Nearnefs to the Glafs.

A Painter may ufe the fame Method for the drawing of Figures, Poftures, &c.
from: Nature, Statues, Relievo’s, and, in fine, every Thing: It being certain,
that a little Practice will render the Method exceeding feafible and eafy. ;

PRACTICAL a

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Another elegant Manner of practifing Perfpective,
without underflanding it.

if a FITS Method is as curious as the former, and fome even prefer it,
by Reafon there is a double Draught required in that, one on the

Glafs, and a fecond copied or imprinted from it. Whereas in the prefent

Method only a fingle Draught is made, and thar as exactly as the former.

I fhall not deferibe the Structure of this Inftrument, it being the fame
with that already mentioned; excepting that the Frame, inftead of a Glafs
fitted in it, muft be divided into a Number of little Squares by fine Threads

drawn at equal Diftances from each Side of the Frame, acrofs each other,
forming what wecall a Reticula, or Lettice. - As to the Number of Squares,
it is left to Difcretion: All we need add is, that they muft not: be too
large that you may work the more exa@ly, nor too {mall for Fear of
being confufed. :

For the Practice, place the Piece H in fuch Manner as that you may
fee all the Objeats you mean to defign, thro’ the Hole of the Sight I. If
the Defign fhould be larger than the Compafs of the Frame, or Reticula,
or Checquer, Squares muft be made on the Cloth, or Paper, larger than
thofe of the Frame. If the Defign be intended fmaller on the Cloth, €ec,
than the Frame is, make the Squares lefs; otherwife they are to be of
the fame Size. But in all the Cafes make the fame Number of Squares
onthe Paper, &c. as you fee in the Frame when you look through the
Sight I. Thus, transferring proportionally from the Squares in the one,
to the correfponding ones in the other, the Perfpective will be as juft as if
you had gone by the ftri& Rules, and ufed the Compafs, Ruler, Gc.

Thetwo Figures fhew how the Piece H is to be placed, in order to de-
fignona Table. The Expedientis of excellent Ufe in Painting, and ferves
to draw very exactly, any Perfpective Draught, to copy Paintings, draw

to the Life, ¢c. ;
' Some People will be apt to urge, that the Method is not new ; there
being few Painters but what know how to enlarge or diminifh Paintings
by Means of the Checquer, or Squares. All this we muft allow, bur
amuft take the Liberty to fay, that we don’t know of any that ever yet ufed
the Sight; which, however, is the great Means of doing any Thing in
Perfection.

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FIGURES

Perfpective DRAUGHTS, PAINTINGS, and
RELIEVO’.

SAR Sam BRe Ss Pa sees

RSPEGTIVE

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Figures in Perfpeétives.

H AVING now thewn to draw all Kinds of Perfpetives, with their Ornaments, and other Cireum-
ftances neceflary to pleafe the Eye, there remains nothing to deceive it entirely, but to add Figures.
But before we go farther, we mutt diftinguifh between Figures, it being one Thing to reprefent a Hi-
ftory, and another to aim to deceive the Eye by a Piece occafionally placed in a Gallery, Hall, Garden,
or the like. In thefe latter, ftill Figures do beft, whereas in a Hiftory-Piece they muft all be, as it were,
animated by the Diverfity of their Poftures, be.

The Number of Horizons which our Painters frequently introduce in the fame Piece, leads them in
to an Infinity of Faults, in not being able to give the Figures their proper Heights, proportionate to
their Eforizons. I hall therefore here give a fingle Rule, which may prevent their failing, be the Ho-
rizon what it will.

For Figures that have the Eye in the Horizon,

J N Perfpeétive Draughts placed at the End of a Gallery, Hall, Walk, or the like Place, to deceive

re the Eye, the Horizon foould always be its natural Height, that is, five Foot, which is that of an or-
inary Size.

_ And Figures intended to appear there as natural muft have the Eyein the Horizon: For, having the

Eyes in the fame Horizon with ourfelves, they will be of our own Height, This might be let pafs as

fafficient Inftruétion, ‘but to make the Point yet clear and more obvious, I fhall inftance’ in thefe three

Figures, inftead of twenty others which might be brought.

The firft Figure A is thenatural Height, and has its Byes in the Horizon. If a fecond Figure be re-
quired in the Place B, from the Point B a Perpendicular mutt be raifed to the Horizon, and it will ap-
pear of the fame Height with the former. If you reqnire a third at C, let his Eyes likewife be in
the Horizon, and he will be the fame Height with the reft, in Appearance. In Effett, tho’ there were a
Thoufand, there need no other Rule be regarded, when the Horizon is the natural Height. I muft
not here be underftood as including Children, which are to be made in Proportion to the large Figures,
according to the Difcretion of the Painter.

| For Figures that have a low Horizon,

N Paintings for Halls, which are ufually hung pretty high, ¢he Horizon moft be dower, to bring it as
near the ye as poffible.

Now, to give each Figure its juft Height and Proportion in whatever Pert of the Painting it be,
fome one mutt be drawn of any Height at Pleafare, in any Part of the Piece, 2 the Figure DF, which
is here to do the Office of a Line of Elevation.

And to find the Height of the other Figures in the Painting which are to appear as high as the firft,
draw Lines from the Head and Feet of this Figure D F, toa Point in the intaded Horizon, as E, and
within this Triangle D E F, will be found the Heights of all the reft. ‘Thus, e. gr. if the Height ofa
Figure in the Point G be required, from that Point G I draw a Parallel to the Bafe G H, till it inter-
feét the Line, or Ray DE inthe Point I, and the Perpendicular HI gives the Height of the Figure,
which is to be taken in the Compaffes, and fet off in the Point G. If anothe: be requiredin the Point
K, the fame Operation is to be repeated, and we fhall have the Perpendicular MN for the juft Height.
And fo of the reft.

122

PRACTICAL

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For Figures that have a high Florizon.

Wee the Horizon is high, as we are fometimes obliged to make it, in
order to reprefent an Object viewed from fome Eminence, the fame Rule
already laid down for a low Horizon mutt be obfervcd, all the Figures in the for-
mer Cafe being above the firft, and all lefs and lefs; and in the prefent Cafe all
- Of them likewife raifed above the firft, and the remoteft always the higheft, and
. at the fame Time the fmalleft in Proportion.

Having drawn the firft Figure, AB, draw a Line from the Top of its Head,.
and the Bottom of its Feet, to fome Point in the Horizon, asthe Point C, then
will all the Heights of the other Figures be taken within this Triangle A CB,
For Example, if you would have the Height of the Figure in the Point D, from
D draw a Parallel to the Bafe Line D E, as far as the Line AC, which will give
the Point E, from which a Perpendicular is to be raifed as far as the Line B C,
which will give the Point F. This Perpendicular, EF, will be the Height of a
Figure inthe Point F. If a Figure be required in the Point G, the fame is to:
be done as for D, and you will have the Perpendicular HI, for the Height of
the FigureG. By the fame Method the Heights of all other Figures in any
other Places may be taken.

for Figures that have their Feet in the Horizon.

Tis but rare that Figures are made above the Horizon, but where there 1S. a:

Neceffity for it, thofe intended to appear the foremoft mutt be made the.
largeft, that is, they muft be made the natural Height, and all the reft being
made lefs, as they are more remote, will appear equal tothem. Thus the Fi-
gure K 1 is here the biggeft and the neareft, and MN the remoteft. All the
Secret here, is in the Painters finifhing the front Figures more than thofe behind,
and ftill the farther off they are, the feinter and lefs perfect muft they be.

The Rule for thefe F igures, and for thofe which have their Eyes in the Hori
zon, is no other than their own Height. - For in each Way, all you have to re-
gard, is to make them lefs, and feinter asthey are thrown farther behind, :

PRACTICAL

124 PERSPECTIVE

EHS SAIN DGD ODOM S IMT EV GINS 29
CES CSI SIRES LORS 9 CS SIRE SIISS IRA CSSD

Figures railed above the Plan.
H ERE are fome who hold, that Objects

raifed above the Ground are more diminifh’d
than if they were on the Plan; and, of Confe-

quence, a Figure mounted four or five Foot fhould |

be fmaller than if on the Earth. And the Rule
is good for Figures a great Height, as fhall be
fhewn in its Place: ButaRife, like that juft men-
tioned, can only make an infenfible Diminution.
For fuppofing fuch an Objet, or Figure, may be
feen at one fingle View, that is, without raifing
the Eye, it muft be the fame Height when rais’‘d,
as when on the Ground. Thus, the Figure A
muft be the fame Height as B, and the Figure C
as D, and F equal to G, and fo of the reft.

The fame Reafon holds for Figures below the
Plan, which are to be reprefented of the fame
Height as thofe above it, as is fhewn in Figure EB,
which is equal in Height with H and I, and as
bigasK. Thefe two Examples may ferve for all
Cafes. 3

PRACTICAL

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125 PERSPECTIVE

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The Poftures of Figures in Perfpective.

od HERE mutt be adeal of Choice in the Poftures, or Attitudes of the Figures,
to deceive the Eye. For ’tis not all of them are good, as we have already
obferved. This Confideration has determined me to add a few, which may
pave the Way for the Invention of numerous others.

The firft is a Man who reads, ftanding ; the fecond is reading an Advertife-
ment pofted on the Wall; the third plays on a Lute; the fourth is afleep ; the
fifth is lolling, with his Back turned on the reft, who are ranged two by two;
thofe marked 6, are looking on a Draught on Paper; the remoter, mark’d 7,
are in earneft Difcourfe. One might addothers, playing, fpeaking, or difcour{-
ing at Table, writing, praying, ce. In Effect, you havea Choice of an Infinity
of Poftures, provided they be fuch as that a Man may continue *em for a Time.
But never ufe fuch as are much in Action; for you can never be deceived in fee-
ing a Leg or an Arm inthe Air, or a Perfon running without fhifting his Place.

ERBRERBRRR RRR BBR RR GSES

Beasts avd Birpvs im Perfpective.

By a fame Rules muft here be obferved as in human Figures, giving each
the Height or Breadth of the firft, and from the two Ends of this firft
Meafure drawing Lines to the Horizon for the Mealures of all the reft.. For
Example, having intended the firft Horfe, A D, to be the Height of that other,
B, from the Line AD draw a Line to the Horizon C, and from B draw a Pa-
rallel to the Bafe Line BK, till fuch Timeas it cut the Line AC, which will give
the. Point K; from which a Perpendicular, K L, being erected, will give the
Height of the Horfe in the Point B.

As to Birds: From the Extremities of their Wings, F F, you are to draw Lines
to the Horizon, and between thofe Lines to take the Dimenfions of the reft, which
we fuppofe of the fame Size. For Example, to have the Magnitude of a Bird in
the PointG, draw a Parallel to the Bafe Line, GH, till fuch Time as it cut the
Rays EandF, which will give the Line HI for the Magnitude of the Bird G.

When Beafts or Birds are required, you muft always make Choice of fuch as
arethe ftilleft, or leaft active, as a Dog fleeping, or gnawing a Bone, a Cat
‘watching a Moufe, a Parrot, &c. ,

PRACTICAL 126

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126 PERSPECTIVE

PASS ISPISPISPISEIS TTB SSPOSISEIS INO OSS OS IS ISS ISNT
POTOIOTOSOGO ER AY GSE IS A SOOO TOOT hg

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HAGLER SSASSSES BORD SOS OME SNE BRE

To find the Height of remote Figures, whereof the
Sirft ts on a Mountain near the Eye.

{t isa Thing that gives a deal of Satisfaction to the Mind, when a Perfor
knows what he does: On which account the Reader will be well enough
pleafed to have the following Rule, which few Practitioners are acquainted withal.

When fuch Figures are to be made determine the Height of the firit, that
is, the Space of the Ground you would have it rais’d; and at that diftance put
another Figure underneath, of the fame Height as the firft ; and from the Feet
and Head thereof draw Lines to the Horizon; by which you will have the
Height of the other Figures in the Champain. To explain myfelf:

The Figure A, for Example, which is a-top gt a Mountain, is five Foot high,
which is the natural Height ; andI fuppofe the Mountain twenty-five Foot high:
If now a Man be rais’d twenty Foot, as is the Piece in the Middle, whereon the
Spectator is mounted (who himfelf is fuppos’d five Foot high) the Horizon will
be twenty-five Foot as well as the Mountain; and confequently will rafe the Top
of the Mountain: As is expreffed in the Figure.

Now to find the Height of the little People in the Champain make a Fi-
gure twenty-five Foot lower, underneath the Figure A, or in fome other Place,
as BC; and fromthe Feet B, and the Head C, draw Lines to fome Place in
the Horizon, as the Point O; and between thofe two Lines, B and C, drawn
to O, take the Height of the little Figures, as already taught. Thus, for the
Height of the Figure D, draw a Parallel to the Bafe-Line, till it cut the Line B
in the Point E; from which a Perpendicular is to be rais’d, cutting the Line
€ O in the Point F: And take the Height of this Perpendicular E F, for the
Height of the Figure in the Point D. If you likewife require the Height of the
Figures in the Point Gand H, proceed after the fame manner as in the Figure
D, and you will have their Heights between the Lines Band C; to be taken in the
Compafies, and fet off inthe PointsG and H. ‘The fame you are to do for any
other Figures, ftill diminifhing, fill at length you come to a mere Point.

This is all we have to fay as tothe Meafures of Figures in Perfpective: But
as Ihave ingap’d myfelf to give all the Meafures of this Kind, the following
Rules come in my way, though they have no ftrict Relation to that Art.

PRACTI€AL © 126

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DENENEHENED COHEMEDENEVED
IDOL IZOD GIO CHD DEDED

To give the natural or any other Height to Figures much elevated.

i ie omit nothing relating to the Heights of Figures we add the two following Rules: The firft
given by Albert Durer, Serlio, and others, for writing of Letters on eminent Places; fo as they
may appear of the fame Size as thofe at Bottom. But for the fame reafon it may be applied to find the
Meafures and Magnitude of Figures which fhall appear equal when view’d froma certain Place wherein
the Spectator is.

Thus in B there: is a Man five Foot high, and fifty diftant from. the Tower A, viewing the firft Figure
C, which there appears of the natural Size ; and thirty Foot higher another Figure is to be placed, which
thall appear of the fame Size as the other, when view’d from the fame Place. Now, to find its Di-
menfions defcribe a Quadrant of a Circle, or a leffer Arch, on a Paper to be placed before the Eyes;
then looking at the Feet, and the reft of the Figure C, it will give the Diftance or Angle, EF, on the
Paper. This done without moving the Quadrant look at the Point D, where the Foot of the Figure
D Lis to be; and obferve what Point it gives in the Quadrant, viz..G. And from this Point G fet of
the fame Diftance or Angle, as that of the Figure C, wiz. EF, which being remov’d to G gives G H.
Then looking through the PointH, note what Part of the Perpendicular rais’d from D is cut thereby,
wiz. the Point I, then will the Interval D I, be the Height requir’d for the Figure to be placed there.
If you would have another ftill higher the fame Operation mutt be repeated, and they will all appear of
the natural Bignels to the Spectator, B. ;

If you require the Reafon thereof you muft recolle& the Principles already laid down, or recur to
them again ; and you will find that all Objeéts view’d under equal Angles appear equal. Now’tis cer-
tain, that the Angle G H is equal to EF ;. confequently the Figure DI muft appear equal to the Figure C.

REE EH ROAR ARH OB CBI CEILI CBHI CBN ABI NC?
To find in what Proportion equal Figures grow lefs to the Eye, when placed

over one another.

i HE Speétator K having a Quadrant, or part of a Cirele, like that of the firft Figure B,. looks to-
wards the firft Figure M of the Tower L;. which there appears of the natural Size. Then
taking its Meafure from Head to Foot he marks the Diftance thereof on the Quadrant, viz. N O.
After this, without ftirring out of his Place, he direéts his Eye to the Head of Figure P, and marks the
Angle it. gives on his Quadrant, viz. QR. And if there be others till higher, he would take them all
after the fame manner, and lay them down on his Quadrant.

Now to find the Difference between the one and the other take the Angles or Diftances of each in
your Compaffes, and you will find that the higheft gives the fmalleft Angle; and of confequence fhew
the fmalleit Figures to the Eye ; foas the Figure P fhallonly appear half the Figure M, tho’ the one be
in reality as bigas the other. If you ask the Reafon, weanfwer, that the Angle of Figure P is only
half that of the Figure M 3 as you fee that Q R is only half of N O, or nearly fo.

By this Knowledge we may arrive at thatabove, and by that above we can come at this : For if M
and P be the fame Magnitude, and yet P only appear below to be half of M, we may fecurely fay, that
to make P appear as bigas M, it muft be twice its prefent Magnitude. The fame may be faid of the
uppér Figure, where D, which is double to C, appears no bigger to aSpeétator in B than C does. It
might be added, that unlefs D were bigger than C, it would only appear half asbig ; fo that one Rule
is the reverfe of the other. Both the firft and fecond Rules are beft put in practice by the little Foot, as
the Figures hitherto have been; by which we come at the Difference and Proportion of Figures as {e-
curely as if they were taken from the Life by a Quadrant.

PRACTICAL 329

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PERSPECTIVE
Bn te te ee se ee es eo
Meafures for elevated Figures.

EF ROM what we have been faying of the Diminution of Figures when placed on high; we are te
take our Meafures in Proportion, for fuch as are to be rais’d in Paintings, whether they be placed
on Mountains, Houfes, or above the Clouds in the Air. The two Rules we have now to give, will
render the Method extremely eafy.

For the firft, I fuppofe the Man A to be fix Foot; which Height I fet off feveral times on a Perpen-
dicular B, over the Bafe-Line ; and from the fevera! Divifions 6, 12, 18, &c. draw Lines to the Head of
the Figure A. Then fetting one Point of the Compaffes in the Point A, with the other I defcribe the
Arch C D, and the Interfeétions that Arch makes with the Rays, are the Meafures to be given the Fi-
gures. Thus, if I would havea Figure appear forty two Foot high ; I take E D, which cuts the two laft
Rays, and fet it off toF, which is forty two Foot above the fame Bafe-Line A B. If another be re-
quir'd thirty Foot high ; the Diftance G H muft be took, which cuts the Rays 30, 36, and gives the
Height of the Figure P ; and fo of the reft. The main Point is the appreaching or receding of the Line
B; which muft always be the Diftance between the Spectator and the Objeét, viz. here, thirty Foot, or
thereabout.

For the fecond Rule: Inftead of the Line B, us’d in the firft Figure, I here put the Divifion from fix
Feet to fix on the Bafe-Line I T. The two firft Points I and 6 are to be drawn to the Point of Sight
K. Thus between the two Rays I K, and 6 K, we have the Meafure of fix Foot, which is the Height
to be given the Figures. Then from all the other Divifions 12, 18, 24, 30, €¥c. draw Lines to the
Point of Diftance L, and in the Interfections made with the Ray 6 K, draw little Parallels to the Bafe-
Line, between the RaysI K, and 6 K. Thefe Parallels will give the Heights of Figures unequally
high, but at the fame Diftance. Which may be prov’d by comparing the Meafures of the firft Method
with thofe of the fecond.

If it be ask’d how much each Figure is diminifh’d from the firft, which is fix Foot high, you need
only to take the Height of the Figure requir’d in your Compaffes, and fet it off on the little Scale M,
and the Queftion is folv’d. Thus, having taken the Height of the Figure B, and fet it on the Scale M, it
gives four Feet ; which fhews, that a Figure fix Foot high, rais’d thirty Foot, will only appear to be four
Foot. The Heights or Diminution of the reft are found by the fame Operation ; provided the Diftance
be the fame with that of thefe. If the Diftance be chang’d the Procefs muft be begun anew.

The Figures V, X, Y, which are in the Clouds in the fecond Figure underneath, are of the fame
Height and Proportion as in the firft Figure. They are only here added to fhew, that tho’ the Method
be different the Effeéts are-the fame, ;

What has been faid as to the Heights and Diminutions of Figures on the Bafe-Line A B in the firft
Method, and I T in the fecond, muft be obferv’d in Proportion as they are funk farther behind; And
the higheft muft have the fame Relation to thofe under Ground which are in the fame Line, as this F P
to that A. Thus, in the fecond Rule, if over-againft the Jaft Figure N there were another Figure O,
placed on a ‘Tower forty-eight or fifty Foot high, and its Magnitude requir’d, it muft be put in the
fame Proportion as N hasto I. And inafmuch as the laft N only contains two and a half of the fix
Parts which I contains, this O upon the Tower muft only have two and a half of the fix Parts in the
Figure N. If I would have another Figure, R, on another Tower, forty-eight or fifty Foot before the
Figure Q, I take two Parts and a half of the Figure Q for the Height of the Figure. If another were
requir'd in S, which is thirty Foot high, in the fame ‘Tower he muft take four of the fix Parts of the
Figure Q, that is, four Foot; asalready mentioned in the firft Method between the Rays G andH.

What renders this Rule the more valuable is, that all the Proportions of Figures may be learnt by
heart. . For whoever would be at the trouble of making this Meafure, where he might add more Parts,
they would ferve him for ever ; and he would render them fo familiar, that in a little time he would tell
you off hand, that if you are thirty five Foot diftant, and the Figure fix Foot, or fix Parts high, when
on the Ground, another, that fhall be of the fame Size, will only appear five Foot and a half when rais'd
to the Height of twelve Foot ; only five, if rais’d eighteen Foot ; only four and a half, if twenty-four
Foot ; only four, if thirty ; only three, if thirty-fix ; and only twoand ahalf, if forty-two: And fo
_on, by fix and fix, to any Number at Pleafure. 4

PRACTICAL 128

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MET Hee DS

Of finding the

NATURALSHADOWS

OBE. 1S

Sun, CANDLE, Torcu, and Lamp.

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Origin of SHADOWS,

it. O define a natural Shadow, we do not call it an abfolute Privation of all

Light, for this would be toform a perfect Obfcurity, wherein Objects would
be no more feen. than their Shadows: But we mean by Shadow, a Diminution of
Light, occafioned by the Inter pofition of fome opaque Body, which receiving and
intercepting’the Light that fhould be-caft on the, Plane it is placed on, there. gives
a Shadow of itsown Form. For Light being of a communicative Nature, <dif-
fufes itfelf on every Thing not hid from it, particularly on every Thing that is
plain and fmooth. But where there happens the leaft Elevation, a Shadow is
produced, which exhibits the Figure of the illumin’d Part on the Plan.

The Diverfity of Luminaries occafions a Difference of Shadows; for if the
Body thay iHumines be larger.than the-Body illumined,.the Shadow will be lefs
than the Body. If they be equal, the Shadow willbe equal to the illumined,
andif the Luminary be lefs than the Obje&t, the Shadow will be continually en-
larging as it goes farther off,

The better to comprehend this, we here add three Figures, which may ferve as
4 Foundation for all the Rules to be:advanced hereafter.

The firft fhews, that the luminous Body AB, being larger than the illumined
CD, enlightens more than half the Object, and givesa pointed or conical Sha-
dow, whereof the Luminary is-the Bafe.. This Truth is evinced in an, Eclipfe of
the Moon, which is rarely quite covered by the Shadew of the Earth, tho’ the
latter be above forty Times the bigger. The Reafon is, that the Sun, which is
the Luminary, is one hundred and fixty Times bigger than the Earth, which
therefore it illumines more than half, and of Confequence makes its Shadow ter-
minate in a Point. |

The fecond having the luminous Body, FG, equal tothe illumined HI, half
the Object is enlightened, and ics Shadow projected parallel, HI KL.

The third fhews, that the Luminary, or Light, M, being lefs than the “illu-
mined N O, the latter is not half enlightened. And of Confequence the Shadow
NOPQ enlarging as it recedes farther from the Object, makes a Pyramid,
whereof the Luminary is the Point, or Vertex.

PRACTICAL,

2

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130 " PERSPECTIVE

Of the Difference of Shadows.

ROM what has been obferved in the preceding Page we draw this

Conclufion, That the fame Object may project Shadows of divers
Forms, tho ftill illumined onsthe fame Side, the Sun giving one Form,
_ the Torch another, and the Day-light no precife Form at all,

The Sun always makes its Shadow equal te the Object, that is, projects it
parallel-wife, as in the firft Figure.

How this Method is to be put in Prattice, and each Object have its
natural Shadow, fhall be fhewn hereafter, “Tis certainly of Confequence
to all Painters, Engravers, &c, to obferve thefe Rules precifely, and nat
take the Rules for Candles, Lamps, or the like, in Lieu thereof, as is too
frequently done, |

The Shadow of a Torch or Flambeau, is not projected in Parallels, but
in Rays proceeding from a Center; whence, the Shadow is never
equal ta the Body, but always bigger, and grows bigger as it recedes the
farther, This is fhewn in the fecond Figure, where the Shadow is larger
than in the firft, tho’ the Cubes of the ane and the other be of equal
Breadth and Height, It appears, therefore, a grofs Abufe, to reprefent
the Shadow of a Torch like that of the Sun, and the Shadow of the Sun
like that of a Candle, ‘when the Difference is fo confiderable,

Lhere is a third Kind of Shadow, neither produced by the Sun nor
a Torch, butonly a fine funny Day, which wanting Strength to finifh and
define its Form occafions a Dimnefs near the Object, as in the third
Figure, Now for this there is na certain Rule, but every Body conducts
it at Diferetion,

All thefe Shadows,«both thofe of the Sun, of the Torch, and of the
Day-light, mutt appear darker than the Parts of Objects not illumined,
Thus A is lefs dark than B, by Reafon A receives the Reflexion of the
Brightnefs around it, and B has no Reflexion but fram A, whichadelf
is in Obfeurity, It muft be obferved by the Way, that the Part Gf the
Shadow moft remote from the Object is ftill darker than that neareft it;
as Gis darker than H, by Reafon A cannot communicate the little Reflexie
onit receives, as faras G, tho’ it does to H,

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131 PERSPREE TEV &

LALA AAARA A EERRS
To find the Form of the Shadows.

T may be remembred, that at the Beginning of this Book, Perfpetive
was defined, The Art of reprefenting Obje€ts which are on the Ground,
or a horizontal Plane, upon a Plane perpendicular to the Horizon. But
inthe Bufinefs of Shadows it is quite the reverfe, fince we there conceive
a Body raifed over the Plan, which being illumined, cafts its own Shadow
onthe Plan; as we find the Body A gives a Shadow B, onthe Plan.

To find a Shadow two Things are fuppofed, vzz. Light and a Body.
Light, tho’ quite contrary to Shadow, is yet what gives it its Being, as
the Body, or Obje@, is what gives its Form and Figure. “What we have
here is to confider the Shadows, the Reader being fuppofed already inftructed
in what reiates to putting the Bodies in Perfpective.

Toconceive the Nature of Shadows more clearly, and render the Prac-
tice more eafy, ic muft be obferved, that there are two Points to be made
ufe of. One of them the Foot of the Light, which is always taken on
the Plan the Obje& is placed upon, the other, the luminous Body: The
Rule being common to the Sun, Torch, @c. with this Difference, that
the Sun’s Shadow is projected in Parallels, and that of the Torch in Rays,
from the fame Center. We begin with that of the Torch, as leading
toa more eafy Underftanding of that of the Sun, which follows.

We fay then, for Example, that if “tis defired to have the Shadow of
the Cube A, here reprefented in B, Lines muft be drawn from O, the
Foot of the Luminary, through all the Angles of the Plan of the Ob-
ject, ashere OD, OE, OF, OG. Then other Lines are to be drawn
from the Point of the Light of the Torch C, through all the fame An-
gles, till they interfect the Lines fromthe PointO. ‘Thus, having drawn
a Line from O through the Angle D, another muft be drawn through
the fame Angle, interfecting the former in H, which Point H-will be the
Shadow of that Angle. And if from the fame Point C, the fame be
done through all the Angles, the Lines of the Plan will be cut in the
Points H, I, K, L, which being conneéted together by right Lines, you
will have the Shadow of -the Cube, as is fhewn in the Figure above, and
more diftinély in that below,

131

PRACTICAL

132. PERSPECTIVE

CQORRYEBHOD ORR MBH OGORBIERF OS ERI ERH
Shadows from the Sun, .

TT HE Sun, that magnificent Luminary, being vaftly larger than the
whole Globe of the Earth, as has been already intimated, muft give
all its Shadows pointed, by Reafon it always illumines more than half of
them.

In Confequence of this Demonftration we might conclude, that all the
Sun’s Shadows mutt be lefs than the Bodies that project them, and dimi-
nifh more and more as they recede farther and farther, Now this would
be true, were there any Relation between the illumin’d Body and the
Iluminer ; but as all Objeéts on the Earth are fo fmall, in Comparifon of
that Star, the Diminution of their Shadows is imperceptible to the Eye,
which fees them always equal, 7. ¢. neither broader nor narrower than the
Body that forms them. On this Account all the Shadows caufed by the
Sun are made in Parallels, as is fhewn in the fecond Figure of this
Treatife.

From the whole it appears, that to find the Shadow of any Body what-
ever, oppofed to the Sun, a Line muft be drawn from the Top of the Lu-
minary perpendicular to the Place where the Foot of the Luminary is to
be taken. and thro’ this Place an occult Line to be drawn through one of
the Angles of the Plan of the Obje&, and another from the Sun to the
fame Angle; the Interfeétion of the two Lines will exprefs how far the
Shadow istogo. All the other Lines muft be drawn parallel hereto.

For an Example, to take the Shadow of the Cube A, the Sun being
in B, from the Bottom of the SunC, which is, as it were, the Foot of
the Light, draw a Line thro’ one of the Angles of the Plan, as CD. Then
from the other Angles E, draw Parallels to this Line. And to find the
Extreme of the Shadow draw a Line from the Sun, B, through the An-
gle F, cutting the Line CD in G. Then drawing a Parallel to this Line,
through the Angle H, it will cut the Line E in the Point I, and give the
Shadow of the Cube, DGI. x

If you defire to havethe Shadows caft forward, or any other particular
Way, you have only to determine the Place of the Sun, and the Point be-
neathit, todraw the Lines of the fame Angle, and the other Lines parallel
thereto. The Methodis the fame as in the former Cafe, fo that it needs
not be repzated, The Figure fhews the reft.

PRACTICAL 132 :

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The Shadows of the Sun are equal in Objects of the
fame Fleight, tho’ at a Diftance from each other.

XPERIENCE teaches us, that feveral Styles or Elevations of

the fame Height, remov’d to a diftance from each other, do yet
project equal Shadows at the fame time: We fay in the fametime, for they
are lengthening and fhortning, in proportion as yhe Sun comes nearer or
recedes farther off; one or other of which he is continully doing.

For this reafon, when the Shadow of an Object is to be caft any way,
you muft determine the Place of the Sun, and the Point underneath, to
draw two.occult Lines from the fame, for the Extremity of the Shadow ;
as here the Pallifade A gives the Extreme of its Shadow in B: And if
from this Point B, you draw a Line to the Point of Sight C, this Line
B Cwill be the Shadow of the Pallifade D, ‘as well as of that of A, and
of all the reft in the fame Line to the very Point of Sight. In Effeé,
it muft be held for a certain Maxim, that Shadows always retain the
fame Point of Sight as the Objects.

On the footing of this Obfervation, that Objects of the fame Height
give equal Shadows, if you would give the Shadow of the Pallifades
E,.F, which are the fame Height as A, D; take in your Compaffes the
Diftance A, D, and fet it on the Foot of the Pallifade E, by which you
will have E G; then from G draw a Line to the Point of Sight G:
And thus you are to proceed, though the Walks were infinite.

If the Light come from the Middle, or Fore-part, as in the Figure
underneath, the Method muft not be alter'd; but only the Foot, or
Bottom of the Sun, to be brought nearer or farther off, and Lines
drawn from each thro’ an Angle: Thus H and I give the Extreme of
the Shadow of the Pallifade K, in the Point L; and from La Line muft
_ be drawn to the Point of Sight M: Then from all the Angles of the

Plan of the Pallifade, Parallels to be drawn to the Line H, as far as
the Ray L M; and the natural Shadow of the fame Pallifade will be

given. 4.

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PRACTICA LE,

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Of Shadows, when the Sun is diretly oppos’d to
the Eye.

S often as the Sun is before the Eye, that is, directly over the Point of
Sight, the Sides of the Shadow it produces will be Parallels, as all the
Vifual Rays-are.. For this Reafon, the Point of Sight is always to ferve for the
Foot of the Light; and the other Ray, that is to determine the Shadow, will be
taken from the Centre of the Sun.

Thus the Shadow of the Cube A being requir’d, draw Lines thro’ all the An-
gles of its Plan B C, tothe Point of Sight D, as the Lines BE and CF. Then,
from the Center of the Sun, G, draw two Rays, cutting the former in the Points
K and L, and paffing thro? the Extremes of the Lines rais*d from the Angles B.
andC; viz. H andI. By this means the Shadow. of the Cube will be found
BKLC.

The Shadows of the two other Objects,.M and N, are found by the fame
Rule,. and fo might as many others as fhould be feen there,

But my Mind fugegefts, that there might be fome Difficulty, if, inftead of a
Cube, a Pyramid were given ; by reafon the Ray from the Middle of the Pyra-
mid, and that from theSun, paffing thro’ its Vertex, or Point, only make
ene Line; and, of confequence, cannot terminate any Thing for the Shadow
of the Vertex of that Pyramid.

When this happens, draw a Line from the Point of Sight P, thro” one of the
Angles of the Plan; by which means you will have OQ. Then from Overeé a
Perpendicular O S, and from the Point of the Pyramid T draw a Parallel to the
Bafe, till ic cut the Perpendicular O'S inthe Point V. Draw the Ray of the
Sun thro’ this Point,. and continue ic till it cut the Ray O Z.in the Point X;
from X draw a Parallel to the Bafe, as far as the Ray of the Middle of the Py-
ramid, which will be cut thereby in the Point Y, the Extreme of the Shadow..
To Y draw Lines from the Angles Zand O}; and the Triangles ZY O will be
the Shadow of the Pyramid.

The like you are todo for the oppofite Face,. if it be perpendicular to the
Plan ; and the fame Rule will ferve in all Cafes. For Example, if the Point, or
Apex, correfpond to the Centre of the Plan, draw a Line from the fame°*Cen-.
ter parallel to the Bafe, and of any Length at Difcretion ; and from the End of
the Line, as here from OQ, drawa Line to the Point of Sight, and proceed as be-
fore. Which will bea ftanding Rule, whether the Pyramid be view’d in front
or fide-wife. And hence you will eafily judge what is to be done, if the Point,
or Vertex, correfpond to any other Ray of the middle of the Plan.

The Walls in the Front of each Figure have their Shadows as already taught
in that of the Cube A.

PRA GT UOC AW 134. |

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135 PERS PE G6 TINGE

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For the Shadows of perforated ObjeE#s.

¥7 HEN the Object is fquare, or retilinear, Lines muft be drawn
W from the Foot of the Luminary through all the Angles of the
Plane ; then from the Middle of the Sun B, drawa Line to the remoteft
Angle C, which will cut the Line from A, in the Point D; through
which Point a Line muft be drawn from the Point of Sight, till it meet
the laft Line from the Plan F. To find the reft of the Shadows; draw
Parallels to the Bafe BCD, through the Angles GHI; and inafmuch
as the Sun illuminates two Sides, or Faces, and makes the Shadow
broader, as is fhewn in the firft Figure, where GC and HI are the
_ Diagonal of the fquare Pieces; where thefe Lines drawn through G C
and H I cut the Line A, a Line muft. be drawn to the Point of Sight E;
and you will have the whole Projection, or Shadow of the Object.

If it be a round Obje&, as reprefented in the fecond Figure, a Cir-
cle muft be defcrib’d, according to the Rule given for Arches in Pag.
62, 63. by erecting of Perpendiculars, &c. . And when the Circle is
form’d, and its Thicknefles given, from the Bottom of thofe Perpendi-
culars, Parallels to the Bafe muft be drawn; as here K L. Then tak-
ing L, which is. the Parallel of the Middle of the Circle, for the Foot
of the Luminary, from the Middle of the Sun, M, draw a Line paf-
fing over the Circle N, and continue it till ic cuts the Parallel L in the
Point O; which will be the Extremity of the Shadow. ‘The Vacuity,
or Aperture, of the Rotundo, is found by drawing a Parallel to N O
from the Point P, which is the Top of the Obje@ oppofite to the Sun,
till ic cut che Line 1O. The reft of the Rotundo will be found by
drawing another little Parallel to N O from the Point R, which will
give S, The reft of the round Obje& is found by drawing Parallels to
NO, through all the Points of the Circle of Perpendiculars, which are
to be continued till they cut the Parallels to the Bafe-Line; as is here
done for that of the Middle, L O. I could eafily mark them all with
Points, but Lam too great an Enemy to Confufion,

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136

P
RAAAARSARAAR
SCCEEECLCECETEL

Shadows affume the Form of the Planes they are
caft upon. i

“VITHERT O we have confider’d Shadows on an even Plane; being fecuré

that a Perfon, who underftands fuch, will find no Difficulty in the Practice

of the reft which follow: For the Rule is the fame in all; and one fingle Inftruc-
tion will fuffice to fhew how Shadows fink and rife according as their Planes are.

To fhew that thefe Shadows are form’d by the fame Rule as the preceding
ones, draw a Line from the Foot of the Luminary A, through the Pian of the
Door B 3 and another from the Sun C, over the Top of the Door D; thefe
Lines will interfect each other, tho’ without the Limits of our Page, and give the
Extremity of the Shadow 3; as already is obferv’d of the others. But the Wall
E preventing the Line A B from being continued as it fhould be, if the Plane
were even, obliges it to rife, as we fee in F G: For this reafon the.Sun’s Ray,
which fhould proceed to meet the Line A B, cuts it on the Wall in the Point G,
and there marks the Form or Shadow of the Door; the Top whereof is drawn
to the Point of Sight H.

The Shadow of the Object K is caft in all its Length KI, and paffes over
that other L: And it is to be obferv’d, that the Shadow ttill preferves its
Length, though it meets with fomething between the two: and that the Shadow
which pafies over any thing affumes the Figure of the fame thing ; as here the
Shadow of Mand N, take the Form of the Obje& L.

Though I have made the Sun to appear in all my Figures, it muft not be ima-
gin’d that he is fo near the Obj cts. My Intention was to fhew that the Rays
proceed from him when at fuch a Height, tho’ far without the Limits of the Piece.
As in this fecond Figure, which yet has the Line for the Foot of the Sun A B,
and that of the Rays of the Sun C; by reafon thofe are always required for finding
the Extremities of the Shadow.

The Shadow of the Object O is found by continuing the Line AB, and
making it rife over the Steps, and againft the Wall, till cut by the Ray in the
Point S, by the Rays paffing over the Corner of the Obje@; and from S draw-
ing a Line tothe Point of Sight T,

To find the Shadow of the Obje& P it muft be remember’d, which has al-
ready been obferv’d, that the Foot of the Light muft alwzys be fuppos’d on the
Plan where the Object is placed. Accordingly, the Ray C cutting the little Line

1B, fhews how far the Shadow of the little Obje&t, P, muft go, to be thence
lrawn to the Point of Sight T.

FS Object V cafts its Shadow all along, tho’ in ics way it defcends into a
itch,

The Shadow of the Wall, R, is found by the fame Rule as the reft; as aps

pears from the Lines A B, and the Ray C. 4

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HASUADHST SCHOO SS USNS Hs VOS PSSA SSSe SSS HSs

To find the Shadows of Objects broader at Top than
‘ | at Bottom.

W HEN the Projeétion or Shadow of a Figure is requir'd,
whofe Top is broader or wider than the Bottom, asin
the two adjoining Figures, the ufual Method is, to makea Plan,
and draw Perpendiculars, as BA, BA, from the fame. The
Plan finifh’d, a Line muft be drawn underneath the Sun, as
_ already mentioned, and Parallels to this Line be drawn from all
the Angles of the Plan. Then a Line to be drawn from the
SunC, over one of the Anglesof the Object, as D, till it cut
the Line of the Plan of the fame Angle A, fo as to. form the
Line DF. Another Line is to be drawn over the Angle A,
till it interfe&s the Line BA in the Point F. Then drawing
Lines from E and F to the Point of Sight, you will have the
Shadow of the Square of the pp of the Object. Laftly,
drawing Lines from the Point of the Figure H, tothe Points
F and L, you will have the Shadow of the whole Figure,
which isa Pyramid inverted.

’Tis evident that the Projection or Shadow of the Crofs un-
derneath is performed after the fame Manner, which it would
be unneceflary to repeat. 3

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138 PERSPECTIVE

BE GVILNGRVAGINGISG AIL GASs
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To find the Shadows of Objects fufpended from the

Ground.

oe HE Method is rendered very eafy by that juft laid down, all-you have to
do in each being to find the Plan, and from that Plan to draw Parallels to
the Line from under the Sun, through all the Angles, and then, from the fame
Angles of the Objects fufpended in the Air, to draw other Lines, cutting thofe
drawn from the Plan; by which Means you will find the Extremes of the Sha-
dows, asalready mentioned under the preceding Figures. =

Tam clearly perfuaded, therefore, that my Reader would eafily conceive any
Thing that I can do asto Shadows made by the Sun, without any farther. Expla-
nation of the Figures here annexed, as being all intelligible, and performed by
the Rules already taught. Bt

However, as every Thing has fomething particular in it, it may not be im-
ded to take Notice thereof, that there may benothing but what is eafily under-

ood.
I obferve then, that in the firft Figure the Plan ABCD is alone made ufe of,
to find the Shadows of the Objects EF, by Reafon they are both on the fame
Line, and of the fame Height.

In the fecond, it muft be obferved, that the Piece of Wood G cafting its Sha-
dow on the Wall H, that Shadow makes the fame Figure at the Cornice I under-
neath. And the fame is obfervable of the Stick K, raifed againft the Wall H.

To find the Shadow of the Board L, the Rule already delivered for Objects
broader at Top than at Bottom, muft be remembered; for having drawn the
Perpendicular M, where it cuts the Ray NO, you muft draw the Line from:
underneath the Sun MP. Then from the Board L, drawing a Line to cut the
Line MP, the Point of Interfection will be the Extremity of the Shadow.

The Shadow of the Globe or Ball Q is likewife found by letting fall two:
Perpendiculars, of which the Plan is to be formed, then through the Center of
this Plan drawing a Line from beneath the Sun, R, anda Tangent from the
Sun, as QS, till it cur the Line R in the Point T, and laftly, another, as V,.
cutting the fame Line R: This Interval T V_ will give the Extent of the Shadow
of the Ball. 3

PRACTICAL a.

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To find the Sun’s Shadow for human Figures.

HE Shadow of thefe Figures is found by the fame Methods as thofe of

other Bodies, that is, by Parallels both from underneath the Figure, and
from the Sun; with this Difference only, that the Shadow of other Bodies, or
Objeéts, is found by Means of their Plan, whereas Figures have none. But in
Lieu of fuch Plans, a Line muft be drawn underneath the Figure, and on this
Line, the feveral remarkable Points of the Figure to be let fall perpendicularly,
which Line is to ferve asa Plan. ;

Foran Example, in a Figure naked, or dreffed without a Cloak or Gown, as the
firft Figure hereto adjoining, with its Back towards us; from under its Feet,
as A, draw aLine to the Point of Sight B, and to this Line AB draw occult
Lines from all the Points that may contribute to the true Shadow ; thus from the
Hand C, let fall a Perpendicular, cutting the Line A B in the Point D, and
from the Elbow E let fall another to the Point F, and a third from the
Head Gro the Point -H, and from all thefe Points DF H, as alfo from the
End of the Staff I, draw Parallels to the Bafe Line. :

Then, having determined the Height of the Sun, a Line muft be drawn from
the fame, as K, pafling over the Edge of the Hat G, and- continued till it cut
the Line H in the Point L, which will be the Extreme of the Shadow. And
again, from the hind Edge of the Hat M, draw a Parallel toK GL, till it like-
wife cut the Line H in the Point N, thefe two Points N and L, will be the Sha-
dow of the Hat. A third Parallel muft be drawn thro’ the Point C, till it cut
the Line D inthe Point O, this Point O will be the Shadow of the Hand that
holds the Staff; drawing therefore a Line from the Point O,-to the Point I,
the Line O I will be the Shadow of the Staff. A fourth Parallel to be drawn
thro’ the Point E, which cutting F in P, will be the Shadow of the Elbow. The
fame do fromall the other Parts, as the Knees, the Feet, €%c. Thefe feveral
Points connected together, give the Shadow of the whole Figure. The Shadow
of the little Figure Q is done by the fame Method. I have not exprefied all
the Points and Parallels therein, in order to avoid Confufion.

To find the Shadows of Figures clothed in long Garments; draw a Line from un-
der their Feet to the Point of Sight, as here the Line SR, and thro’ the Bot-
tom of the Robe draw two Parallels to the Bafe Line, each Way, asthe Lines T
and V, and between the two, another Line X for the Middle of the Figure. Then
from the Top of the Head draw a Line Y, for the Ray of the Sun, to be con-
tinued till it cut the Line X in the Point Z; which Point Z will be the Extreme
where the Shadow is to terminate. The reft of the Shadow will be drawn be-
tween thetwo Parallels T and V. If any Thing comes over them, as the two
Plaits; or Folds, + and *, they muft be drawn by Parallels to Y-Z, till they cut

the Ray V. And thus t+ gives the Shadow of. the Elbow, and * that of the Folds
of the Gown.

PRACTICAL,

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PERSPECT EHV E

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An cafy Method of finding the Shadow of the Sun.

ERE TI here to add the Shadows of all the Objeéts that might be given,

it would be a Work without End, Objects being multipliable to Infinity ;
In Effeét, befides the Greatnefs of their Number, each particular one might
furnifh out a whole Book, as being capable to be turned, inclined, and difpofed
in various Manners, each of which has its feveral Shadows. But the Labour
would be ufelefs, inafmuch as every Body will be prepared to make any at Plea-
fure, provided he be Mafter of two or three Rulesalready laid down for the Sha-
dows of Objeéts taken from the Sun, two Kinds of Lines being fhewn to contain
the Means for finding all Shadows imaginable ; one of the Lines coming from
under the Sun, and paffing over the Plan, and the other proceeding from the Sun
itfelf, and paffing over the Object, and cutting the former Line in the Place where
the Shadow is to terminate. But as thefe Lines are to be all Parallels, that is,
thofe from under the Sun parallel to each other, and thofe from the Sun likewife
parallel among themfelves, it may be neceflary to give a Method of drawing
them with Expedition and Advantage.

I have already fhewn how to draw Parallels to the Bafe by Means of a {quare
Board, as A, anda Ruler B, which fame may ferve to draw the Lines from un-
der the Sun, when found direétly over the Face of the Object, as the Line CD.
But where he illuminates the Object from an Angle, another Inftrument mutt be
ufed, as that here reprefented E, which is a Rule faftened to the End of ano-
ther Piece of Wood, well fquared, and grooved quite through, fo as the Rule
FG may be moveable therein with fome Force, and that having taken an in-
clined Line, as HD, another Parallel thereto IK, may be taken by Means of this
Bevel, which is the Name the Workmen give this moveable Square EF G. This
Inftrument fhortens the Work exceedingly, when Shadows are to be made by the
Sun, on which Occafion there isno Line of any Inclination whatever, but Paral-
lels will be required thereto. The Application will evince its Ufefulnefs. For
Shadows by the Candle or Torch, it is of no Importance, by Reafon all. the
Lines are there drawn froma Center.

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PERSPECTIVE

rei Ow aNd WAY es BE % st NSE . ys .
OCP ire inertia pba ri theca rian hr cae ca ria i a

Shadows from a Torch, Flambeau, Candle,
and Lamp. |

at has been already obferved, that there are two Points requir’d for the find-
A ing of Shadows; the one the Foot of the Flambeau, Candle, Lamp, &e.
Which is always found on the Plane where the Object is placed, the other in the
Fire, or Flameof thofe Luminaries.

From the firft Point, whichis the Foot of the Flambeau, or beneath the Lamp,
&¢, Lines muft be drawn through all the Angles of the Plan of the Object,
whofe Shadow is required ; and the fecond Point gives other Rays, which paf-
fing through the Angles of thofe Objects, interfect the former Lines, and fhew
where the Shadow isto terminate. I fhall illuftrate this by an Example, wherein
the fame Letters fhall be ufed for all the three Luminaries, from which it will
readily appear, that the Praétice is the fame in all: With this only Difference,
that the Foot of the Flambeau or Torch actually ftands on the Plane, and that
the others areonly conceived to do fo. ,

I add then, that if the Shadows B, of the Cubes A be required, Lines mutt
be drawn from the Point O, which is the Foot of the Luminary, thro’ all the
Angles of the Plans of thofe Cubes, asOD, OE, OF, OG, and then from
the Point C, which is the Light or Fire of the Luminaries, other Lines muft be
drawn through the Angles of the Objeéts, and continued till they interfect the
former Lines from O.

Thus, having drawn a Linefrom the Point O, through the Angle of the Plan
D, drawing another Line from C, through the correfpondent Angle of the Ob-
jet P, this latter Line being continued, will cut the firft from the Angle Din
the Point H, which Point will be the Shadow of that Angle DP. From the fame
Point C, do the fame for all the other Angles of the Plan in the Points HIKL,
which Points being connected by right Lines, give the Shadow of the Cubes,
as in the three Figures. From this Inftance it readily appears, that the Method
is the fame in one as another. abies

In the following Page we fhall fhew howto find the Bottoms or Feet of Candles
and Lamps, 2

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PRAUTTICAL

iii OT

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142 PERSPECTIVE

Of the Foot of the Luminary.

INCE the Method of finding Shadows by the Torch, Candle, and Lamp is
S the fame in all, as already obferved, there is no Occafion for difting ui thing
between them in any of the following Rules. For when IF put a Candle, a Torch
or a Lamp might as well be put in ifs Place, the Light of one having the fame
Effeét as that of any of the reft.. So that for the future, we fhall ufe the Word
Light indifferently for all three. :

Asto the Foot of thefe Luminaries, which muft ftand on the Plans where the
Objects are placed, it is found after the following Method.

A lighted Torch being in a Chamber, whether in a Corner, at a Side, or in
the Middle thereof (Inftances of each hereof we have in the ereéted Figure) we
‘mutt confider all the Parts of the Room, wiz. the Cieling, Floor, Sides, €@c. as
having Points wherein the Foot of the Luminary may be placed, and that from
thefe Points Lines may be drawn thro’ all the Angles of the Plan of the Obje&
whofe Shadow is required, as fhall be expreffed more at large in the following
‘Page, my chief Defign in this being to fhew how that Point is to be found.
The Torch then being placed in A, this Point A is the Foot of the Light, and
B the Light or Fire of the Torch, which Fire is there fuppofed immoveable,
tho’ the Foot may be found on all Sides.

To find the Foot of the Luminary on the Side of the Wall C, drawa Paralle}
to the Bafe Line, fromthe Point A, till it cut the Ray DE in the Point F, from
which: Point erect a Perpendicular FG. ‘Then from the Point B, which isthe
Fire, draw another Parallel to the Bafe Line, till it cut FG inthe Point H,
which H will be the Foot of the Luminary ; as if the Torch were laid all along
its Fire ftill remaining in the Point B,

To find the Foot of the fame Luminary on the Cieling, from the Point G
draw a Parallel to the Bafe Line, as GI, and from the Point B erect a Perpen-
dicular to the fame GI; this gives the Point K for the Foot of the Luminary,
as if the Torch were turned upfide down.

’ To find it on the other. Side of the Room, the fame Method muft be obferv’d
as for the Side C, and you will have the Point L.

To find the Foot of the Luminary in the Middle of the Room, draw a Line
from the Point H, to the Point of Sight, till ic cut the Perpendicular E in the
Point M. Then from M draw a Parallel to the Bafe Line, interfecting the Torch
in the Point N3 this Point will be the Foot of the Luminary for the Middle of
the Room. ;

The Foot of a Candle is found after the fame. Manner as that of a Torch, ta-
king the Middle of the Foot of the Candleftick forthe Foot of the Luminary ;
but when it is a Plate, or an Arm fixed in the Wall,..’tis this Arm or Branch,
that determines the Line where the Foot of the Luminary fhall be. For In-
ftance, in the Plate P, through the Arm Q, draw a Perpendicular to the Bafe
Line as RS. Then from the Fire T, draw alittle Parallel to the Bafe Line,
which cutting RS in the Point V, gives the Foot of the Luminary for that Side.
The Point X will be the Foot for the Floor ; the Point Y for the Cieling, and
Z for the front Wall of the Room.

As to Lamps, ’tis the Place they are hung in that determines the Foot, as
here the Charaéter*; from which Place a Parallel to the Bafe Line is drawn as
far as the firft Ray, &c. The reft the fame as in the Torch or Candle,

i eee ee a i a

PRACTICAL 142

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UML ee ON ene eR TR nT THOUENSLAS TE PARADA ASE
= INET aa: e os

eo PERSPECTIVE

To find the Shadows of a Torch on all the Sides of a Room.
Tt HE Shadows taken from the Sunalways tend towards the Earth, by Rea-
fon that Star never gives us any of its Light, but when above our Hori-
zon, and of Confequence raifed above our ordinary Objects, and fo occafioning,
their Shadows to defcend. But the Cafe is different in Torches, Candles, and
Lamps, which may be placed either above, below, or afide of Objects, and
therefore may yield Shadows on all Sides, as we are now to fhew.

The preceding Figure will help to find the Shadows of Objects difpofed on
all Sides of the Room, for having found the Foot ef the Luminary as already
directed, there is nothing difficult behind, the Method throughout being the
fame with that for the Cube in Pag. 141. to which Recourfe may behad. Fiow-
ever, to fave you the Trouble of going fo far back, I fhall here obferve, that to
find the Shadow of the Table the Torch is placed in, you muft draw Lines from
the Foot of the Torch A, thro’ all the Feet of the Table C. Then from the
Point of Light B, draw Lines over all the Points of the Table 1, 1,1, &c. till
they interfect the Rays C,C, &ec. in the Points O, O, €$¢. which will give the
Bounds of the Shadow of the Table.

The Shadow of the Object D is found by drawing Lines from the Point A,
through all the Angles of the Plan, as far as the Angle of the Wall D, and from
that Angle raifing them perpendicularly, Then from the Point of the Light
B, drawing Lines over the Object D, and obferving the Angles correfponding
to the Lines of the Plan, you will have the Shadow F of the Object D, |

The Shadows of all the other Pieces are found after the fame Manner; So that
all we fhall here note, is the Foot of the Luminary, the Fire itfelf being fup-
pofed to be fixed in the Point B. :

For finding the Shadow of Figure G, the Point L is the Foot of the Luminary.

To find the Shadow of Figure N, the Point H is the Foot of the Luminary.

To find the Shadows of the Figures I and M, the Point K is the Foot of the
Luminary.

For the fecond Figure, having found the Foot of the Luminary on all the Sides
of a Room, as directed in the preceding Page, the Shadows of Objects are found
in any Place at Pleafure by the Rule now delivered. For Example, having found
the Foot of the Luminary Q, and its Fire P, if you would have the Shadow of
the Object R, draw Rays from the Point Q, over the Plan of Objeét, continuing
them indefinitely. But inafmuch as they meet with the Wall, or Side of the
Room T, in the Places S and S, where they meet the fame, they muft all be
raifed; then drawing other Lines from P, over the fame Object R, they will
cut thofe of the Plan, and mark the Place of the Shadow upon each, obferving
that the Angles refer to the Lines drawn from the Plan.

This Method is fo univerfa], that a Man who only knows how to take the
Shadow of a Cube, will make no Difficulty of finding the Shadow of any other
Objeét whatever. “For this Reafon, having defcribed that Method for the Cube
in Pag. 141. and added this above, which in Effect is the fame; I imagine Ihave
siven abundant Inftruétion for the managing of all Shadows, and may be excufed
from repeating thé fame in the feveral Figures following. Wherein all I fhall
note, is the Poimtfor the Foot of the Luminary.

To find the Shadow of the Figure V, the Point X is the Foot of the Luminary.

To find the Shadow of Figure Y, the Point Z is the Foot of the Luminary.

To find the Shadow of the Figure --, the Point & is the Foot of the Lumi-
nary. Pis the Fire, or Light itfelf, for all the Objects in the fecond Figure.

PRACTICAL 143

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144 PERSPECTIVE

REBEL IRERELEFE LIS ER EVE ESE OEE EES BEES & &
aan HIS SPP PRAY GUN A ADL B39 AS ISIE TI

= % Cafercareaoate Caper! gfe Cafes) USS ES ASS EAS 3S ps eS CS 1CICAERCS 9 & € Jo Stercan 6. gat
CEH SI SS SS SS SS SSS SOS SS Se eS x

The Shadow of an erett and inverted Pyramid
by Torch-light.

fe Bas E Shadow of an ere&t Pyramid by Torch-light, falls as it would
by the Light of the Sun, and‘in both Cafes there is but one Line,
wherein the vertical Point of the Pyramid will be found. Upon the
Plane BC DE draw the Diagonals EB, and DC, through the central
Point F, raife the Perpendicular FA, and from the four Points BC DE,
draw Lines to the Point A, and the Pyramid will be ere@ed. Then, to
find its Shadow, draw an indefinite Line from the Bafis G, of the illumi-
nating Body, pafling through F, and from the central Flame of the
Torch H draw another Line over the Vertex of the Pyramid in the Line
GF, til ic cut the Point J, which Point will limit the Shadow of the
Pyramid. Laftly, draw a Line from C to I, and another from Eto I,
and the Triangle CI E will be the Shadow of the Pyramid.

To gain the Shadow of an inverted Pyramid, draw perpendicular Lines
from the angular Points of its Bafe, and form the fubjacent Plane by
Means thereof, after the Manner directed for the Sun, Pag. 138. And
from all the Angle of this Plane, draw Lines to the .Bafe of the Torch
G, then from H, the central Point of the Flame draw other Lines, touch-
ing all the Angles of the Bafe of the inverted Pyramid, and dividing thofe
of the Plane, whereby the Shadow will be defined; as we before obferved,
in other Inftructions relating to the Torch,

BER ESES SER EASOOS DESL EETS TERS SE
The Shadow of a Grofs.

E before confidered the Shadow of a Crofs by the Sun, let us now
fuppofe the fame Obje@ placed in the Light of a Torch, that we
may find the Difference between the two Cafes. The Conftruction of
the latter is obvious enough, particularly if compared with the Method of

finding the Plane, delivered in Pag. 137. and the other Directions laid
down for Shadows by Torch-light. 2

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144

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148 PERSPECTIVE

a Rgnoeh pened fan oehbgeaeg fan nth ae aff ares fae eegsaeathaaeseg ae
To find the Shadows of round Objects by Torch-light.

J*HERE may feem to be more: Difficulty in reprefenting the Shadows of

Globes, Bottles, Drinking-Veffels, and ‘other bellied Objects, by Torch-
~ jight, than in thofe of fquare ones, but the Directions already given will ferve
for thefe alfo; for there is nothing more required here, but to reduce Squares
to Rounds, as we taught in Pag.19, 20, 28, 29, and 86. which contain all the
neceflary Inftruétions for giving the Plans of round Objects in Perfpective,
whence all other Cafes of that Kind may be eafily underftood. .

We gave in Pag. 138. the Method for finding the Plan of a Ball, and by
Means of that Plan, the precife Magnitude of the Shadow by the’Sun. But as
the Cafe of the Torch differs from that, we fhall be a little more particular upon
the Ball, becaufe ic will facilitate all the other Directions relating to Rounds.

Having by Means of a Pair of Compafles, marked out the great Circle of the
Ball A, draw its Diameter BC, and below this Circle draw a Line parallel to
BC, touching the Circle in the Point H. Then fromthe Extremes of the Dia-
meter BC, let fall Perpendiculars upon the Line below, as BD, and CE, and
with thefe Points Dand E, make a Plan, DEFG, in the ufual Manner, the
Diameter whereof, FG, will divide D E atthe Point H. And this Plan will
ferve to find the Shadow of the Ball A. Now, having drawn from the Batis of
the illuminating Body I, Lines’ touching this Plane on both Sides, as I K and
IL, and another IH M, through the Center of the Plane H, as alfo Lines
from the Center of the Flame N, which touching the Ball’between A and B,
hall divide the Line IH at the Point M: This Point muft terminate the Sha-
dow. To gain the firft Part of this Shadow, draw from the fame Point N,
another Line, touching the Fore-part of the Ball, and dividing alfo the Line
TH at the Point Q, then the Diftances between Q and M will be the Length
of the Shadow. And for its Breadth, draw from the fame Point N, two Lines
touching the Extremes of the Diameter of the Ball Z Z, and dividing the Lines
1K at’the Point R, and ILatthe Point S. Now then, as RSis the Breadth
of the Shadow, and QM the Length of it, if the four Points R, S, Q, M;
be joined with curve Lines, there will be an Oval formed for the Shadow of the
Ball A. .

Ihave been the larger upon this Shadow, becaufe I judge the Direction given
about italone fufficient for finding the other Shadows of Rounds, as of the Ob-
jet V, for Example, which having two unequal Breadths, ought to have a Plan
of two Circles. And the Figure X having-three, fhould have its Plans corre-
fponding thereto, one for the Neck of the Bottle, another for its Belly, and a
third forits Foot; all whichare to be made as thofe for the Ball.

An Infpection of the Figures will render any farther Explanation. of them.
unneceflary. 2

fae PERSPECTIVE

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Shadows ow feveral parallel Planes.

HE firft Plane here is the Floor whereon the Chair A ftands; the fecond

Plane is the upper Part of the Table, parallel to the firft, and may be
either above or below it. There might alfo be more of thefe Planes wherein to
find the Foot of the illuminating Body, in order to come at the Shadow of the
Object. Suppofe the Foot of the illuminating Body to be C, and the Flame B;
from thefe Points C and Bdraw Lines through the upper and under Part of the
Object D; which will give the Shadow E upon the Table.

To find the Shadow of the Chair A, which is placed onthe Ground ; determine
the Foot of the Luminary on the Table in C, on the Ground: This is clear’d
by the Inftruétions following.

From the Point of Diftance, which is here fuppos’d without the Limits of the
Paper, draw a Line thro’ the Foot of the Table F; then from the Angle Gupon
the Table, let fall Perpendicular; cutting the Line F in the Point F1; and from
Hi draw a Parallel to the Bafe HI, which is equal to the upper Part of the Ta-
ble, and will direct us to the thing requir’d. For, drawing a Line from the Point
of Sight K, through the Foot of the Luminary C, to the Extremity of the Table
L.; fromthe fame Point L, let fall a Perpendicular to HI, which will give the-
Point M. Then from M draw a Line to the Point of Sight K 3. in which Line-
M K will the Foot of the Luminary be found. To determine the precife Point
let fall a Perpendicular from the Point C, which, cutting the LineM K, will give-
the Point N for the Foot of the Luminary. This Point N thus found,. there
will be no Difficulty in finding the Shadow of the Chair A; the Method being.
the fame as for the other Objects taught in the preceding Pages: That is, from.
the Foot of the Luminary N draw Lines through all the Angles of the Plan.
ef the Chair, and other Lines through the upper Part of the Chair, from the
Luminary B; thefe latter by interfecting the former exprefs the Bounds of,
the Shadow. For the reft the Figure gives fufficient Directions.

The fecond Figure is not here added as if there were any particular Circum.
{tances different from thofe of the Figure above, but only to put you upon re-
colle€ting what has been already taught, viz. That Objects caft their Shadows
differently, according to their different Difpofitions about the Luminary. Thus,.
the ‘little Objeéts on the Table project their Shadows this or that way,.as the
Luminary is on this or that Side; as is found from the common Rules relating.
to the Foot of the Luminary, and the Light itfelf. Moft of the Objects: here
reprefented are broader at the Top than Bottoms; fo that ic will be neceffary to.
make Plans thereof, after the manner already fhewn.

146

PRAOTICAL

PER SPE CRIT VE

Shadows of Cielings dy Torch-light.

T HESE Figures are not placed in the Sun’s Light, becaufe that Luminary
is high above all the Objects of the Earth, and confequently can give no
Shadow where the illuminating Body is fuppofed to be under the Object. If it
be faid, tho’ the Sun’s Rays enter a Room, yet the Shadows of Bodies continue
to appear ; I anfwer, that fuch Shadows are not immediately caufed by the. Sun,
but the Brightnefs thereof, and that they cannot be reprefented by parallel
Lines, as thofe of the Sun, but by Rays iffuing from the fame Center, as thofe
of a Torch, taking the reflecting Body for the illuminating Point, and proceed-
ing in drawing fuch a Shadow as in the Cafe of a Torch.

The Direétions hitherto given, which turn upon the forming of Plans, and
drawing of Lines from the Angles of Objects, to find the Bounds of the Sha-
dow, would be too tedious here, and the great Number of Lines neceffary to be
drawn, would render the Figure exceeding intricate, on Account of the feveral
Beams, Supporters, and Rafters that would occur. This Inconvenience drove
me to invent a fhort, eafy, practical Method for the fame Purpofe, without
departing from the Rules of Art.

The Floor being put in Perfpective, as was taught in Pag. 55, and 57. and the
illuminating Body fixed, we muft inquire by Means of the Bafis of that Body
where the illuminating Point ought to be. To find this Point, when the illumit-
nating Body is at B, draw from the Foot of it C, a Parallel to the Bafe DE,
till it cut the Ray EF in the Point G, from this Point G, raife a Perpendicu-
lar GL, and from the Flame of the Torch B draw a Parallel to DE, dividing
the Perpendicular G L at the Point L, and this Point L will give the Place and
Length of the Shadow. tt

For Example, to find the Shadow of the Band A, from the Point L draw a
Line, touching the Vertex of the Angle H, and obferve where this Line L di-
vides the firft Rib, as at the Point I, which is the Place of the Shadow’s Ending.
From this Point draw a Parallel IK, and mark upon the Ribs the Place of the
Shadow O. And to find the Shadow of the Space betwixt them, draw another
Line from the Point L, touching the Vertex of the Angle of the firft Rib M, which
will divide the Angle of the Interval at the Point N. Nowthen, from the Point
N drawa Parallel NP, and you will thence haveall the Shadow Q forthe Beam A,

To find the Shadow of the Joifts, draw a Line from the illuminating Point B,
touching the Angle S, and dividing the Bottom of the Entablature at the Point
T. ‘Proceed thus with all the other Ribs, and the Shadow will appear to be
longer the farther *tis removed from the luminous Body. Then mark upon one
Beam all the Points T, and from the Point of Sight R, draw Lines througheach
of thefe Points, and then the Shadows of all the other Ribs will fall exactly be-
tween the Bands, as we fee in the Points V V.

The fécond Figure is the fame with the former, and differs from it only in
being fhadowed, which would have obfcured the Letters and the fine Lines necef-
fary in the other: Only here the Shadow of the Jaumbs of the Gate muft be

taken from the Footof the illuminating Body, asin X and Y.

PRACTICAL 147

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To find the Shadow by the Foot of the Luminary.

F the Objects be perpendicular to the Bafe Line, and higher than the Flame of
] the Candle A, we need only draw Lines from the Foot of the Luminary
B, thro’ the moft advanced Angles of the Objects, ¢.g. C and D of the Skreen,
Fig. 1. and others from the Angle of the Wall E. Thefe Lines BC, BD, and
BE, give the Place of the Shadow in the Points where the Angles made by the
Leaves of the Skreen, meet the Floor; as alfo the Return of the Wall in the
Point G, from whence Perpendiculars muft be raifed, as GR, which will termi-
nate the Shadows given by the Candle A.

_ The Reafon hereof is, that the Line A B being parallel to the Line CH, D1,
K and EL, occafions the Flame, ¢ what Part foever of the Line A B it be found,
whether on high, in the Middle, or below, to give a like Shadow.

It muft here be obferved, that this Rule only holds good of Objects raifed
above the Flame, as thefe are in the prefent Figure. For fuch as fhew their up-
per Part, as here the Object M, the preceding Rules take Place; that is, Lines
muft be drawn from the Foot and Flame of the Luminary.

The Shadow doubled.

Wi EN two Luminaries fhine on the fame Object, two Shadows muft be pro-
duced, each of the Luminaries occafioning its refpective Shadow, and that
in Proportion to the Circumftances of the Luminary. If {uch Luminaries, when at
equal Diftances be equal, the Shadows themfelves muft be equal; but if there be
any Difproportion, that is, if one of them bea little bigger than the other, or one
of them a little nearer the Objeét than the other, the Shadows will be unequal.
Thus the Objeé O being illumined by two Candles, the one near at Hand in
P, the other farther off in Q, it is evident, the Shadow of the Candle P will
be deeper than that of the Candle Q, as is exprefied in the Figure.

The Rules for fuch Shadows are the fame with thofe already given both for
the Sun and the Torch. 3

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The Shadows of human Figures | of Torch-light.

H AV Ereafon to hope that the Advice given long ago,

notto turn over the Page toa new Figure, before the prece-
ding one be well underftood, has been carefully obferv'd. Sup-
pofing therefore my Reader to have mafter’d what was directed
in Pag. 139. for finding the Shadows of human Figures by
the Sun; I have little to add as to thofe in the prefent Plate;
the Line drawn under them, which I ufe asa Plan, ferving
indifferently in either Cafe. But inafmuch, as the Shadow
projected from a Torch is not equal to the Body, as is the Sha-
dow projected by the Sun, a farther Confideration muft: here
be added, viz. that inftead of drawing the Lines parallel to
one another, they muft here be all drafvn from a Center ;
that is, all the Lines drawn over the Plan muft proceed from
the Foot of the Luminary A, and thofe over and about the Fi-
cure, fromthe Point of the Flame; in like manner as for the
other Shadows of the Torch; which it would be needlefs here
to repeat, the Figure itfelf giving abundant Satisfaction. 2

PRACTICAL.

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The different Difpofitions and Heights of Shatdotos
by Torch-hight.

SH4DoOws from the Sun are all caft the fame Way, and have the

fame Difpofition ; it being impoffible the Sun fhould occafion one
Shadow to tend towards the Eaft, and another towards the Weft, at the
fame time. True, in different times of the Day it makes this Difte-
rence: but never in one and the fame Hour.

But the Torch, Candle, and Lamp, have always this Effet; for in
what Place foever one of thefe Luminaries be found, provided dhere be
a number of Objects about them, the Shadows will be caft various ways;
fome tothe Eaft, fome to the Wett, fome to the North, and others to
the South, according to the Situation of the Objects scat the Lumi-
nary; the Foot of which, here reprefented by A, ferves as a common
Centre, from which they all proceed ; and the Flame here reprefented
by B, Mews where they are to terminate, tho’ at different Diftances; as
* the peatett produce the fhorteft Shadows, and the remoteft the longett.

Tho’ in the fecond Figure the Luminary be not placed in the Mid-
dle, yet the fame Rule obtains, with refpe& to the Shadows, as in-the
former Figure; being all drawn from the Foot of the Luminary C, and
terminated by Lines from the Flame D. |

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